WGU C723 Quantitative Analysis For Business - Pre Assessment

21 A scouting troop has been invited to sell ice cream sandwiches as a fundraiser at the city park July 4th fireworks celebration. The sandwiches will cost one dollar each and will be sold for two dollars each. There are no other costs because the city park has agreed to provide use of facilities and freezers. The scouts will have to dispose of, eat, or give away any ice cream sandwiches that are left over after the event. The following "Payout Table" provides values for the events and alternatives of the ice cream venture. (Value Of Events profit in Dollars) Alternative Inventory 1,000, 1,100, 1,200, 1,300, 1,400 Events Demand 1000(10%), 1100(20%), 1200(40%), 1300(20%), 1400(10%) Expected Value $1,000, A, B, C, D Inventory level, Demand in $, Expected Value 1300, $700, $900, $1100, $1300, $1300, $1,080 What is the missing value for C, which has an expected value of an inventory of 1,300? O $ 1,200 O $ 1,000 O $ 1,080 O $ 1,120

$1,080 cuz (700x.1)+(900x.2)+(1100x.4)+(1300x.2)+(1300x.1)=1080

22 A company offers tax preparation services through a chain of 30 small offices in Kansas. Susan, the VP of marketing, has proposed adding an online app to target college students who want to start a business while they are still in school. According to Susan's data, there has been a 200% increase in new small businesses licensed to owners aged 18 to 22 years. The company has a small information technology (IT) department that has neither the time nor the expertise to build such an app. Therefore, three alternatives are being considered: 1) Outsource the work to an app development company to build the app 2) Sign up as a client of a company that already offers this type of app 3) Expand the IT department by hiring a programmer to develop the app Kevin, the VP of Finance, believes it is more likely that the trend in college students opening small businesses will rapidly decline. He has put together the following table to show the company's estimated profit in the first two years for each alternative. Use the table to calculate the expected values. Alternative Outsource the work Sign up with an app Hire a programmer Decline in trend Likelihood: 80% $4,000 $3,000 -$4,000 Continuing trend Likelihood: 20% $9,000 $6,000 $18,000 What is the highest expected value? O $400 O $3,600 O $6,800 O $5,000

$5,000 cuz (4000x.8)+(9000x.2)=5000 and (3000x.8)+(6000x.2)=3600 and (-4000x.8)+(18000x.2)=400

25 An owner has operated a pet supply store in the same location for more than 20 years. The business has grown each year, and now it must be decided whether to move to a new location across town or renovate the existing store. The owner has just learned that the largest competitor, located across town, has gone out of business. The owner is certain that sales will increase regardless of whether the business is moved or renovated but also realizes that many of the competitors customers may now be willing to drive to the existing location. The following is a decision tree demonstrating the combined potential sales and probabilities for the two outcomes. What is the expected value for expected outcome A (move to new store)? O $625,000 O $312,500 O $250,000 O $1,500,000

$625,000 cuz expected outcome A (move to new store)? is (1000000x.25)+(500000x.75)=625000

Linear Programming Example 4 Which coordinates have highest profit?

(50, 250) - approx. Line 3

Risk vs. Uncertainty

- Risk is an adverse event with a known probability (Measurable Uncertainty) - Uncertainty is an adverse event with an unknown probability (Unmeasurable risk)

8. Y-hat = a + b1X1 + b2X2 + b3X3 + b4X4 The constant is —8, the b1 coefficient is 14, the b2 coefficient is 20, the b3 coefficient is —18, the b4 coefficient is —9, x1 is 1, x2 is 2, x3 is 3 and x4 is 4. What is the predicted value of Y? O 28 O -44 O 64 O -28 O 44

-44 cuz -8+(14x1)+(20x2)+(-18x3)+(-9x4)=-44

43 Consider the following linear programming formulation: MIN 26X1+14X2+12X3 Subject to 2X1+3X2+1X3≥30 6X1+3X2+1X3≥50 X1X2X3≥0 The optimal solution is OBJECTIVE FUNCTION VALUE 1) 228.0000 VARIABLE VALUE REDUCED COST X1 5.000000 26.000000 X2 7.000000 14.000000 X3 0.000000 12.000000 ROW SLACK OR SURPLUS DUAL PRICES 2) 1.000000 0.000000 3) 1.000000 0.000000 What is the optimal value of X3 O 0 O 12 O 5 O 228 O 7

0 cuz variable value reduced cost for x3 is either 0.0 or 12

28 Bob is opening a new location for his popular sandwich shop. The PERT chart for this project is provided below: What is the duration of the critical path for this project? O 14 weeks O 16 weeks O 13 weeks O 27 weeks

16 weeks cuz critical path is the highest value and 10+3+3=16 and 6+4+1+3=14

32. Based on the above network of activities, what is the value for step E, if the path A-B-E-F-G has a total completion time of 17 days? O 2 days O 1 day O 3 days O 4 days

3 days cuz total completion time is 17 days so 17-3-2-6-3=3

16 The histogram below represents the approximate number of packages processed by weight in pounds for a certain zip code at a local mail-sorting facility. Histogram 25----------------- 20-------------------------- 20 15-----------------14---16------ 16 10------------------------------------- 10 5 --------------4 0 Weight/lb: 18 26 34 42 50 58 66 How many packages weighed between 34 and 50 1b inclusive? O 36 O 40 O 50 O 16

36 cuz 16+20=36

10 A hair stylist placed an ad on the home page of the online community shopper website. Daily site visit demographics indicate the following age categories of visitors. Age Category A B C D E F Age Range A Younger than age 18 B Ages 18 to 24 C Ages 25 to 36 D Ages 37 to 51 E Ages 52 to 63 F Age 64 and older Percent of Site Visits A 10 B 13 C 15 D 27 E 21 F 14 What is the probability that either a person in age category D or a person in age category E will view the advertisement, assuming there is no relationship between the site visitors? O 56% O 5.6% O 4.8% O 52% O 48%

48% cuz 27+21=48%

9 What is the value of the following expression? 7^2/3^4 O 2.33^2-4=(1/2.33)*(1/2.33)=5.4289 O 81/49=5.4289 O 49/81=0.6049 O 3^4-2=9 O 7^2-4=1/49=0.2041

49/81 = 0.6049 cuz (7x7)/(3x3x3x3)=.6049

11. A hair stylist used market research to learn that members of different age groups have different preferences for positive and negative advertisements. Research participants could mark their preference for only one of the two ads. The positive ad presented a model with attractive hair supported by a message affirming the decision to schedule hair styling services, whereas the negative ad displayed a model with unattractive hair supported by a message describing the need for hair styling services. Results are shown in the table below: Ad Preferences by Age Category Type of Ad A Younger than age 18 B Ages 18 to 24 C Ages 25 to 36 D Ages 37 to 51 E Ages 52 to 63 F Age 64 and older Positive A 2% Younger than age 18 B 7% Ages 18 to 24 C 10% Ages 25 to 36 D 20% Ages 37 to 51 E 8% Ages 52 to 63 F 4% Age 64 and older Negative A 8% Younger than age 18 B 6% Ages 18 to 24 C 5% Ages 25 to 36 D 7% Ages 37 to 51 E 13% Ages 52 to 63 F 10% Age 64 and older What is the probability of being in the youngest or oldest age categories and having a preference for positive hair styling ads? O 61% O 6% O 24% O 20% O 33%

6% 4% + 2% = 6%

44 Consider the following linear programming formulation: MIN 26X1+14X2+12X3 Subject to 2X1+3X2+1X3≥30 6X1+3X2+1X3≥50 X1X2X3≥0 The optimal solution is OBJECTIVE FUNCTION VALUE 1) 223.3333 VARIABLE VALUE REDUCED COST X1 5.000000 0000000 X2 6.666667 0000000 X3 0.000000 7.333333 ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 -0.500000 3) 0.000000 -4.166667 What is the optimal value of X2? O 0 O 5 O 223.33 O 7.33 O 6.67

6.67 cuz variable value reduced cost for x2 is either 6.6667 or 0

14 A county college has five sections of an Elementary Principles in Finance course and the number of students in each section is as follows: 65 80 93 65 77 What is the mode of this data set? O 76 O 93 O 77 O 65

65 cuz there are 2 65's in the 65, 80, 93, 65, 77 set The mode of a set of data values is the value that appears most often. To find the mean, add up the values in the data set and then divide by the number of values that you added. To find the median, list the values of the data set in numerical order and identify which value appears in the middle of the list.

15 The histogram below represents the approximate weight in kilograms of bags scanned at the check-in counter for a flight on Thanksgiving Day. Histogram: 25 -------------- 20 ----------------------- 20 15--------------- 14 --- 16 -- 16 10--------------------- ---------------10 5-------------4 0---------- Weight/kg: 18 26 34 42 50 58 66 How many bags were scanned? O 20 O 80 O 66 O 50

80 cuz 4+14+16+20+16+10=80

13 A professor selected a recent sample of five students' Introduction to Management midterm grades to perform an analysis. The grades selected were as follows: 70 85 98 70 82 What is the median of this data set? O 70 O 81 O 82 O 98

82 cuz the middle value of the set 70, 70, 82, 85, 98=82 To find the mean, add up the values in the data set and then divide by the number of values that you added. To find the median, list the values of the data set in numerical order and identify which value appears in the middle of the list. To find the mode, identify which value in the data set occurs most often.

7 Y-hat=a+b1X1 +b2X2 The constant is 3, the bl coefficient is 4, the b2 coefficient is —1, X1 is 3, and X2 is 6 What is the predicted value of Y? O 15 O 9 O 11 O 13 O 8

9 cuz 3+(4x3)+(-1x6)=9

35. A construction company was recently hired to renovate the surgical unit of a hospital. The renovation project is quite intricate and will require extensive project management knowledge. The project management team identified various activities and proposed a project with activity times that are provided in the table below: What is the expected completion time for activity A? O 7 days O 9 days O 9.5 days O 14 days

9.5 days cuz A+4D+T -------------------- divided by 6 (7+ (4 x 9) +10) = 7 + 36 + 10 = 57 ---------------- divided by 6 = 9.5 days

34. A restaurant owner wants to remodel her restaurant and hires a project management consultant to plan the project. The consultant identifies various activities that need to be completed and proposes a project network with activity times, which are provided in the table below: What is the expected completion time for activity G? O 7 minutes O 8 minutes O 9 minutes O 9.5 minutes

9.5 minutes cuz G Activity is C=(7+3+2)/3 and E=(11+7+3)/3 so C,E= ((7+3+2)/3+(11+7+3)/3)=11 so (11+12+10+5)/4=9.5

52. A creamery purchases three different types of cheese: panela cheese at $3.75 per pound, goat cheese at $7.10 per pound, and Oaxaca cheese at $4.50 per pound. The daily demand for each cheese is 45, 22, and 63 pounds respectively. The creamery has a dedicated supplier for each type of and the ordering cost is $2.00 per order It is expensive to keep these products in inventory because they are highly perishable. The holding cost is estimated to be 0.5% of the purchasing price for each type of cheese. What is the estimated economic order quantity for the goat cheese? O 95 pounds O 50 pounds O 5 pounds O 951 pounds O 253 pounds

951 pounds cuz per year EOQ = √square root of 2 x set-up cost x demand rate/production cost x interest rate(holding cost) 22lb of cheese per day x 365=8030 lb so √2 x $2.00 x 8030/(.005x7.1) = √904,788.73 = 951.2038333 lb. per year

29. The PERT chart for a project is shown below: What is the critical path for this project? O E-G-J O A-B-J O E-F-J O C-D-F-J O H-I-J

A-B-J cuz the critical path is the highest value so 25+9+5=39

Network Diagrams Example 1 (A) A 6.00 6.50 10.00 Calculate Activity A

Activity A Optimistic A = 6.00 Most Probable M = 6.50 Pessimistic P = 10.00 𝑡 = (6 + (4 x 6.50) + 10) -------------------- divided by 6 Answer = 7.00

Network Diagrams - Crash Activities What is the extra cost incurred when crashing Activity B?

Activity B $35,000 - $25,000 or an additional $10,000 is incurred from crashing

Annual Holding Cost H = i x C Holding cost of inventory is calculated by finding the sum product of the inventory at any instant and the holding cost per unit. It is expressed as follows:

Annual Holding Cost = (Q / 2) x H (or H = i x C) Q: Volume per Order H: Holding Cost (Variable Cost)

Annual Ordering Cost For each order with a fixed cost that is independent of the number of units, S, the annual ordering cost is found by multiplying the number of orders by this fixed cost. It is expressed as:

Annual Ordering Cost = (D / Q) x S D: Annual Quantity Demanded Q: Volume per Order S: Ordering Cost (Fixed Cost)

Total Cost and the Economic Order Quantity Summing the two costs together gives the annual total cost of orders. To find the optimal quantity that minimizes this cost, the annual total cost is differentiated with respect to Q. It is shown as follows:

Annual Total Cost (TC) = ( (D / Q) x S) + ( (Q / 2) x H) or EOQ = dTC / dQ or √ 2SD / H

30. A construction company is working on a project to build a new industrial office park. A local television station was planning to film the construction project and conduct interviews with key stakeholders to create a documentary (activity F), but the filming has just been cancelled. The original PERT chart is shown below: Now that activity F has been cancelled, what is the critical path for this project? O C-G-H-I O B-E-I O B-E-G-H-I O A-D-I

B-E-G-H-I cuz the highest value or critical path is 18+4+6+4+7=39 and 11+4+7=22 and 12+6+4+7=29

Linear Programming Feasible Region - Example 1 Beans: 15 X 1 + 1 X 2 ≤ 800 Tomatoes & Sauce: 6 X 1 + 6 X 2 ≤ 1800 Flavor: 4 X 1 + 2 X 2 ≥ 500 Meat: 5 X 1 + 1 X 2 ≤ 700 Gourmet Chili: X 1 ≥ 0 Campfire Chili: X 2 ≥ 0 Find the feasible region

Beans are a Max so shade away the bad ABOVE the line Tomatoes & Sauce are a Max so shade away the bad ABOVE the line Flavor is a Min so shade away the bad BELOW the line Meat is a Max so shade away the bad ABOVE the line

Decision Tree

Calculate probabilities

Uncertainty

Can not be calculated - so do not worry about it

Decision-Making Model Steps - Step 6

Choose the Best Alternative

6. A marketing manager for a corporation that markets a broad range of food brands needs to plan a monthly marketing, advertising, and sales promotion budget for next year and is looking at monthly sales. One brand shows dramatic fluctuations in sales over the past three years. How should this manager use quantitative analysis to make budgeting decisions for this brand? O Compute quarterly averages based on each month in the quarter O Use last year's budget amounts regardless of average sales values O Compute seasonality indices for each month to forecast next year's monthly sales O Use average sales values for all of the months over the past two years

Compute seasonality (seasonal) indices (indexes) for each month to forecast next year's monthly sales. cuz it will give you visuals to see fluctuations in price over time.

Linear Programming Constraints - Example 3 There are four chili ingredients with constraints. Beans: 15 X1 + 1 X2 ≤ 800 Tomatoes & Sauce: 6 X1 + 6 X2 ≤ 1800 Flavor: 4 X1 + 2 X2 ≥ 500 Meat: 5 X1 + 1 X2 ≤ 700 Gourmet Chili: X1 ≥ 0 Campfire Chili: X2 ≥ 0 Solve for flavor

Consider the Flavor inequality: 4 X1 + 2 X2 ≥ 500. 1. Set X1 = 0. Then we have 4(0) + 2(X2 ) = 500 0 + 2X2 = 500 X2 = 500/2 X2 = 250 2. The X2 intercept is (0, 250). 3. Set X2 = 0. Then we have 4(X1 ) + 2(0) = 500 4X1 + 0 = 500 X1 = 500/4 X1 = 125 4. The X1 intercept is (125, 0). So for Flavor we have endpoints (125, 0) and (0, 250)

Linear Programming Constraints - Example 5 Meat: 5 X1 + 1 X2 ≤ 700 Find the inequalities

Consider the Meat inequality: 5 X1 + 1 X2 ≤ 700. 1. Set X1 = 0. Then we have 5(0) + 1(X2 ) = 700 0 + 1X2 = 700 X2 = 700/1 X2 = 700 2. The X2 intercept is (0, 700). 3. Set X2 = 0. Then we have 5(X1 ) + 1(0) = 700 5X1 + 0 = 700 X1 = 700/5 X1 = 140 4. The X1 intercept is (140, 0). So for Flavor we have endpoints (140, 0) and (0, 700)

Linear Programming Constraints - Example 4 Tomatoes & Sauce: 6 X1 + 6 X2 ≤ 1800

Consider the Tomatoes & Sauce inequality: 6 X1 + 6 X2 ≤ 1800. 1. Set X1 = 0. Then we have 6(0) + 6(X2 ) = 1800 0 + 6X2 = 1800 X2 = 1800/6 X2 = 300 2. The X2 intercept is (0, 300). 3. Set X2 = 0. Then we have 6(X1 ) + 2(0) = 1800 6X1 + 0 = 1800 X1 = 1800/6 X1 = 300 4. The X1 intercept is (300, 0). So for Flavor we have endpoints (300, 0) and (0, 300)

What is Crashing

Crashing an activity is to save time not money. Crashing will increase cost.

Components of the EOQ Formula:

D: Annual Quantity Demanded Q: Volume per Order S: Ordering Cost (Fixed Cost) C: Unit Cost (Variable Cost) H: Holding Cost (Variable Cost) i: Carrying Cost (Interest Rate) T = The Cost To Place The Order S = T x C

EOQ Examples D= 2000 Q = 50 S = $1000 C = $250 H = $25 i = 10%

D= 2000 Q = 50 S = $1000 C = $250 H = $25 i = 10% Q = Volume per Order = 50 Batches per Year = D/Q = 40.0 Annual Order Cost = D/Q x S = $40,000 Annual Holding Cost = Q/2 x H = $625 Annual Total Cost = 40,000 + 625 = Total Cost = $40,625

49. A wholesale distribution company in downtown Chicago sells office supplies. The item with the highest demand is 500-count packages of 20-1b copy paper. The table below contains values for the EOQ model for this item. Based on the spreadsheet variables, which EOQ assumption is correct? O Holding costs remain constant O Order costs remain constant O Demand does not fluctuate. O Lead time does not fluctuate.

Demand does not fluctuate cuz sales quantity is 100,100,100....

Decision-Making Model Steps - Step 2

Establish Decision Criteria

Decision-Making Model Steps - Step 5 (C)

Evaluate the Alternatives - Apply To All

Decision-Making Model Steps - Step 5 (B)

Evaluate the Alternatives - Apply Weight to Each One

Decision-Making Model Steps - Step 5 (A)

Evaluate the Alternatives - Rank Each One

Decision-Making Model Steps - Step 8

Evaluate the Decision

18 A firm that manufactures reusable heating and cooling system filters needs a new supplier for two of the major filtering components. Five potential suppliers have been assessed using scores between 1 and 5, as shown in the following table (the higher score indicates better expected performance): Supplier ID, On-Time Delivery Cost, Cost, Capacity, Total Score Supplier 1 5, 4, 3, 12 Supplier 2 4, 3, 3, 10 Supplier 3 5, 2, 5, 12 Supplier 4 3, 3, 5, 11 Supplier 5 4, 4, 3, 11 Which decision model step does the table represent? O Generating alternatives O Choosing the best alternative O Evaluating alternatives O Listing alternatives

Evaluating alternatives

Decision Tree Example 3 The payoff table provides values and alternatives for the expected t-shirt sales at one location. Based on the information in the table, what is the expected payout for an inventory of 2200 (where (A) is located)?

Expected Payoff for (A) 90 + 300 + 660 + 600 + 180 + 160 = 1990

31. The PERT chart below shows activities and duration's for a project. What is the critical path for this project? O A-B-C-K O I-J-K O F-G-H-K O A-B-D-E-K O F-G-J-K

F-G-J-K = 22+10+15+10 = 57 cuz the critical path is the highest value so A-B-C-K = 20+4+11+10 = 45 A-B-D-E-K = 20+4+2+5+10 = 41 F-G-H-K = 22+10+9+10 = 51 I-J-K = 21+15+10 = 46

Decision-Making Model Steps - Step 4

Generate Alternatives

Holding Cost Holding inventory often comes with its own costs. This cost can be in the form of direct costs incurred by financing the storage of the inventory or the opportunity cost of holding inventory instead of investing the money elsewhere. Therefore, the holding cost per unit is often expressed as the cost per unit multiplied by the interest rate, expressed as follows:

H = i x C H: Holding Cost (Variable Cost) i: Carrying Cost (Interest Rate) C: Unit Cost (Variable Cost)

Network Diagrams - Crash Activities By how much time can Activity H be crashed?

H Inside Painting Normal Time: 3 weeks, Normal Cost: $12,500 Crash Time: 1 week, Crash Cost: $18,500 Time Reduction: 2 weeks H can be crashed for up to 2 weeks. If crashed, H can finish in 1 week.

20. A successful Mexican seafood restaurant in Texas has a single owner and a single location. The owner is debating the next step for the business. The owner thinks that opening only a couple of new locations in the area could help maintain the customers' perception of a unique local restaurant, which has been part of its success. On the other hand, franchising the restaurant could drive rapid economic growth and therefore develop an image as a regional restaurant. It is also possible that a combination of new local locations and franchising could bring better financial and public relations results. This option has the highest associated cost, whereas opening only a couple of new locations or franchising would cost less. In any case, the owner believes the worst-case scenario is to have moderate demand and the best-case scenario is to have high demand. Which major decision is this owner facing? O How to estimate future demand O How to avoid the worst-case scenario O How to expand the business O How to find new locations

How to expand the business

Decision-Making Model Steps - Step 1

Identify the Problem

41. Consider the following linear programming formulation: Max Z=X1+X2 Subject to X1+X2≤4 2X1+5X2≤10 X1X2≥0 The feasible region is shown in the graph. Which graph shows how the first constraint will shift if the resources expressed by the first constraint are increased by one unit?

Image #2 cuz the first constraint (x1+x2≤4) increased by 1 (x1+x2≤4+1) or x1+x2≤5 or (5,5)

Decision-Making Model Steps - Step 7

Implement the Decision

48. Review the graphs below: Which graph represents inventory levels based on receipt of orders of 500 units monthly and a demand of 1,000 pieces per month? O Inventory graph A O Inventory graph D O Inventory graph B O Inventory graph C

Inventory graph B Receipt of orders of 500 units monthly is a downward sloping graph in increments of 500 which graph B indicates. Inventory is declining each month.

47. Review the following inventory graphs, and answer the question that follows. Which graph represents inventory levels based on order quantities of 2,000 pieces received every other month, and demand of 1 ,000 items each month? O Inventory graph D O Inventory graph C O Inventory graph A O Inventory graph B

Inventory graph C net increase/decrease of $1000

4 How should quantitative analysis improve subsequent decision making for a firm that wants to determine whether its revenue has been increasing or decreasing for the past 10 years? O It will help the company see why it has been making a profit O It will let the company determine the average revenue it made. O It will help the company see which customers bought its items. O It will help the company see the competitors' average revenue.

It will let the company determine the average revenue it made. cuz revenue is the question to answer

26 Business is booming at Charlie's bakery. Almost every type of bread sells out daily, and the ovens are at 100% capacity. If Charlie wants to grow his business, he needs more oven capacity to bake more bread. However, he is concerned that if he invests in more capacity, demand may be lower than expected. How would a decision tree help Charlie in this situation? O It would determine the break-even point using what-if analysis in calculating the expected payoff to expand oven capacity. O It would incorporate the probabilities of different demand levels in calculating the expected payoff to expand oven capacity. O It would identify multiple alternatives to determine the highest payoff in order to expand oven capacity. O It would incorporate multiple states of nature for determining which alternative has the highest payoff to expand oven capacity.

It would incorporate the probabilities of different demand levels in calculating the expected payoff to expand oven capacity.

50. A wholesale distribution company in downtown Chicago sells office supplies. The item with the highest demand is 500-count packages of 20-1b copy paper. The table below contains values for the EOQ model for this item. Based on the spreadsheet variables, which EOQ assumption is correct? O Holding costs remain constant O Order costs remain constant O Lead time does not fluctuate. O Demand does not fluctuate.

Lead time does not fluctuate cuz lead time is 3,3,3,....

27 An employee has been asked to decide which machine to choose from four possibilities. The purchase and installation cost for each machine is identical. The decision tree below describes the conditions and expected values. Which machine should this employee select? O Machine B O Machine A O Machine C O Machine D

Machine A cuz Machine A is (100000x.25)+(50000x.75)=62500 highest probability of productivity and Machine B is (100000x.50)+(0x.50)=50000 and Machine C is (50000x.40)+(25000x.60)=35000 and Machine D is (250000x.25)+(-50000x.75)=25000

39. A textile company produces tablecloths and cloth napkins. The production process includes two steps: cutting and sewing. Every day at least 2 production hours must be worked in the cutting department and 6 production hours must be worked in the sewing department. The time needed for cutting and sewing each item as well as the production costs for each item are provided in the table below: Product Time Needed to Cut Fabric | Time Needed to Sew | Production Costs Tablecloths 8 minutes | 9 minutes | $9.50 Cloth Napkins 1.5 minutes | 6 minutes | $3.50 Let X1 represent the number of tablecloths to be produced and let X2 represent the number of cloth napkins to be produced. What is the equation of the objective function Z that optimizes the production cost? O Max Z=2X1+6X2 O Min Z=19X1+13.50X2 O Min Z=9.50X1+3.50X2 O Max Z=9.50X1+3.50X2 O Min Z=17X1+7.50X2

Min Z = 9.50X1 + 3.50X2 cuz X1 goes with tablecloths production cost $9.50, and X2 goes with cloth napkins production cloths $3.50, and Min is at least 2 hours must be worked into the day

40 A manufacturing plant produces exactly 10 tons of a combination of three products per day. The production costs are five, four, and three dollars for products one, two, and three, respectively. The plant works 480 minutes per day. Each ton of product one, two, and three requires 45, 50, and 55 minutes of processing time, respectively. What is the correct linear programming model for minimizing the production cost? O Min Z=5X1+4X2+3X3 Subject to X1+X2+X3=10 45XI+50X2+55X3≤480 X1X2X3≥0

Min Z=5X1 + 4X2 + 3X3 Subject to X1 + X2 + X3 = 10 45X1 + 50X2 + 55X3 ≤ 480 X1, X2, X3 ≥ 0 Cuz 10 tons (equals) of combination of three products = X1 + X2 + X3 = 10 and less than or no more than 480 minutes worked 45X1 + 50X2 + 55X3 ≤ 480

12 A restaurant review blogger uses a product to collect • the number of page views, date, and time of page views; • the number of followers who are alerted by email each time the blogger posts a new restaurant review; • the number of impressions (appearances onscreen) each visual advertisement earns each day or week; • the number of times a visual ad is clicked and the user is taken to an outside website; • the number of times a link is clicked and the user is taken to an outside website; and • various audience characteristics such as use of a mobile or regular computer the ZIP code (location) of the access device, and time of day the engagement occurred per user. After 26 weeks of data collection, the blogger believes there is supporting evidence to charge fees for ad and link placement, which until now has been offered free to a dozen restaurants. Results are reflected in the graph below: Number of New Followers Per Week 14 . 12 . . . 10 . . . . . . 8 . . . . . . . . . 6 . . . . . . . . 4 . . . . 2 . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Week Number (June - December) What does the above graph indicate about new followers? O The number of new followers tends to strongly and steadily grow. O The number of new followers of the blog is decreasing over time. O New followers tend to follow the blog on a seasonal basis. O New followers tend to follow the blog on a cyclical basis. O New followers tend to follow the blog on a random basis.

New followers tend to follow the blog on a random basis. cuz graph looks random

53. A well-known professional taxidermist pursuing an MBA degree is planning a strategy for restocking the chemicals inventory. There is a yearly demand of 24 gallons of polyester resin. The ordering cost per order is $10 and the holding cost per gallon each year is $0.83. In the past, the taxidermist ordered only the monthly demand of two gallons per month. However, after a quantitative methods class, the taxidermist decided to estimate the economic order quantity. Which decision should this taxidermist make to minimize the total inventory cost when ordering? O Ordering twice a month O Ordering once a month O Ordering once a year O Ordering twice a year

Ordering once a year cuz your minimizing inventory cost twice a month = 12 orders x 10 = $120 once a month = 6 orders x 10 = $60 once a year = 1 order x 10 = $10 twice a year = 2 orders x 10 = $20 Total Inventory cost = 24X + (0.83 x 24 x cost-XX) = 24X + 19.92XX e.g. Twice a month = (24 x 120) + 19.92XX

Decision Tree Example 1 - Conclusion e.g. Strong Sales x Probability $10 million x 0.75

Pick option with the highest expected value

17 Patients' Testing vs. Length of Stay 16 . . . 14 ... 12 . . 10 . . . . 8 . . . 6 . . 4 . . 2 . . 0 10 20 30 40 50 60 The scatter-plot above represents the number of tests administered to a patient in a hospital versus the patient's length of stay in the hospital. What relationship can you determine between the number of tests given and the length of stay? O Positive correlation O No correlation O Linear correlation O Negative correlation

Positive correlation cuz a positive correlation is a relationship between two variables where if one variable increases, the other one also increases. A positive correlation also exists if one decreases and the other also decreases.

2 Over the last three months, a small rural hospital has seen a sudden increase in the number of patients coming to the emergency room for non-emergency treatment. The hospital administrator wants to know why there is a sudden increase in demand and is considering three options to find out. Classify each method available to the administrator as qualitative or quantitative. Answer options may be used more than once or not at all. Select your answers from the pull-down list. Including an open-ended question on the intake form asking patients, "Please explain why you selected this ER for treatment." Intake forms can be sorted into non-emergency and emergency categories; the "non-emergency" responses can be analyzed to determine reasons the hospital was selected = Qualitative Pulling the hospital's records for the last 10 years and sorting by medical codes to check for similar patterns in past years. A regression model can be built using non-emergency treatments as the dependent variable, and various independent variables can be tested, such as population change and unemployment levels. = Quantitative Group brainstorming with the nurses and doctors in the hospital to see what ideas people have for why so many people are suddenly coming to the ER for non-emergency treatment. = Qualitative

Qualitative cuz a why you selected question is an opinion. Qualitative or Quality=Opinion Quantitative - Pulling data cuz the question can be counted like 1+2+3+4+5=15. Quantitative or Quantity=Number Qualitative - Brainstorming ER visits. Qualitative or Quality=Opinion

1 A car stereo company is planning to introduce a new product into the market. It faces stiff competition from two other organizations with similar products. The company's marketing manager has asked the production manager to perform a break-even analysis using three different price points. The marketing manager will use the results to set a price for the new product. Which type of method is a break-even analysis? O Expert judgment O Quantitative O Qualitative O Payback table

Quantitative cuz break-even analysis using price points involves numbers Quantitative or Quantity=Number

3. A local music store that hosts live music has been a very popular hangout for years. However, the owner is concerned that the increasing popularity of new methods of music delivery will soon make the business obsolete. The owner is considering building a small recording studio in the basement of the store. The nearest professional studio is 50 miles away, so a new studio may appeal to local musicians and increase foot traffic. The owner has all the costs of building the studio and has also estimated how much revenue might increase due to the new studio (from studio rental fees, increased food and drink sales if more people come to the live music shows, etc.). The owner will use this information to determine the net present value for the studio. Which method of analysis should this owner use to make a determination? O Decision tree O Expert judgment O Quantitative O Qualitative

Quantitative cuz counting number cost of building, food, drink, etc. Quantitative or Quantity=Number.

Decision Tree Example 2 At Location A the expected profit in a good economy is $8 million and in a weak economy is $1 million. At location B the expected profit in a good economy is $7.5 million and in a weak economy is $2.5 million. At location C the expected profit in a good economy is $6 million and in a weak economy is $2 million. The likelihood of a good economy is 65% (and the likelihood of a weak economy is 35%). Which Location has the best results?

Result = Location B Calculate the expected profit for the data in the table in the same way it is done with the data in the decision tree. A = 8mil x 65% + 1mil x 35% B = 7.5mil x 65% + 2.5 mil x 35% C = 6mil x 65% + 2mil x 35% Loc. A = 5.2mil + 350K = 5.5Mil Loc. B = 4.875mil + 875K = 5.75Mil Loc. C= 3.9mil + 700K = 4.6Mil

Risk

Risk Can be calculated

Network Diagrams Example 3 - Find Length of Missing Path D Let ADEGJ = 28 Weeks

Since A + E + G + J = 5 + 4 + 2 + 4 = 15 weeks and ADEGJ = 28 weeks, we can calculate D = 28 - 15 = 13 weeks.

Linear Programming Constraints - Example 2 There are four chili ingredients with constraints. Beans: 15 X1 + 1 X2 ≤ 800 Tomatoes & Sauce: 6 X1 + 6 X2 ≤ 1800 Flavor: 4 X1 + 2 X2 ≥ 500 Meat: 5 X1 + 1 X2 ≤ 700 Gourmet Chili: X1 ≥ 0 Campfire Chili: X2 ≥ 0 Solve for beans

Solve for Beans Consider the Beans inequality: 15 X1 + 1 X2 ≤ 800. 1. Set X1 = 0. Then we have 15(0) + 1(X2) = 800 0 + X2 = 800 X2 = 800 2. The X2 -intercept is (0, 800). 3. Set X2 = 0. Then we have 15(X1) + 1(0) = 800 15(X1) + 0 = 800 X1 = 800/15 X1 = 53.33 4. The X1 intercept is (53.33, 0). So for Beans we have endpoints (53.33, 0) and (0, 800)

Network Diagrams Example 1 - Start Ts4U is expanding and needs to build another office building. The following table lists the activities that need to be completed in order to build the additional office building. The table also shows three estimates for the time it will take the contractor (and sub-contractors) to complete each activity. Using Weeks.

Start with formula: 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝑇𝑖𝑚𝑒 = 𝑡 = 𝐴 + 4𝑀 + 𝑃 ------------------- Divided by 6

33 Based on the above network of activities, what is the value for step F, if path A-B-F-J has a total completion time of 12 days? O 5 days O 4 days O 7 days O 6 days

Step F = 7 days Total completion time is 12 days so 12 - 1 - 2 - 2 = 7 days

Linear Programming Example 3 - Move Profit Line to the left The West Coast Chili Company makes an expensive Gourmet Chili and a less expensive Campfire Chili, the rugged and rustic blend. They want to maximize profits while addressing the constraints to make these two brands of chili. Profits for the Gourmet Chili are $250 per batch while profits for the Campfire Chili are $150 per batch. We want to maximize profits. Using coordinates (50, 0) or (0, 96.67)

The Profit DECREASES Max Z = 250X1 + 150X2 = 250 x 50 + 150 x 0 = 12,500 + 0 = $12,500

Linear Programming Example 2 - Move Profit Line to the Right The West Coast Chili Company makes an expensive Gourmet Chili and a less expensive Campfire Chili, the rugged and rustic blend. They want to maximize profits while addressing the constraints to make these two brands of chili. Profits for the Gourmet Chili are $250 per batch while profits for the Campfire Chili are $150 per batch. We want to maximize profits. Using coordinates (300,0) or (0, 500)

The Profit INCREASES Max Z = 250X1 + 150X2 = 250 x 0 + 150 x 500 = 0 + 75000 = $75,000 (profit)

45 A sporting goods company makes sports bandanas and flags. It costs $10 to produce one bandana and $12 to produce one flag. It takes 1/4 yard of material to make one bandana and 1/2 yard of material to make one flag. What is the constraint in this scenario? O The number of flags produced O The amount of material needed to make one bandana O The amount of material available O The number of bandanas produced

The amount of material available cuz the material constraint is a limitation or restriction.

Network Diagrams Example 2 - Find Paths | Critical Path

The four paths are: 1. ABCJ = 7 + 7.5 + 14 + 2 = 30.5 Weeks 2. ABIJ = 7 + 7.5 + 3.5 + 2 = 20 Weeks 3. ADFGHJ = 7 + 6.5 + 2.5 + 5 + 3 + 2 = 26 Weeks 4. AEFGHJ = 7 + 5.5 + 2.5 + 5 + 3 + 2 = 25 Weeks The critical path is the LONGEST path (in time) so ABCJ is the critical path.

46 Larry owns a boutique that sells handmade table lamps, consisting of one lamp base and one lamp shade. It takes Larry one hour to assemble and wire one lamp base and one hour to assemble and paint one lampshade. Larry works six hours per day, performs all the work by himself, and needs to make an identical number of lamp bases and lamp shades. What is the constraint in this scenario? O The need to make an identical number of lamp bases and shades O The time required to assemble and paint one lamp shade O The number of hours Larry works per day O The time required to assemble and wire one lamp base

The number of hours Larry works per day cuz hours work constraint is a limitation or restriction.

36 Based on the above chart, what is the maximum benefit of crashing both activities C and D? O The project time will be reduced by 8 days. O The project time will be reduced by 2 days. O The project time will be reduced by 35 days O The project time will be reduced by 14 days

The project time will be reduced by 14 days cuz Maximum Time Reduction for C and D is 6+8=14

38. Based on the above chart, what would be the maximum benefit of a project manager crashing activity D? O The cost of the project will decrease by $8,000. O The project time will be reduced by 20 days O The project time will be reduced by 8 days. O The cost of the project will decrease by $33,000.

The project time will be reduced by 8 days cuz Maximum Time Reduction for D is 8

Decision-Making Model Steps

There are 8 Steps - See Chart

Linear Programming Constraints - Example 1 There are four chili ingredients with constraints. The Gourmet Chili requires 15 units of Beans, 6 units of Tomatoes and Sauce, 4 units of Flavor, and 5 units of Meat per batch. The Campfire Chili requires 1 unit of Beans, 6 units of Tomatoes and Sauce, 2 units of Flavor, and 1 unit of Meat per batch. The West Coast Chili Company must use at most 800 units of Beans, at most 1800 units of Tomatoes and Sauce, and at most 700 units of Meat. Furthermore, the company must use at least 500 units of Flavor

There are four chili ingredients with constraints. Beans: 15 X1 + 1 X2 ≤ 800 Tomatoes & Sauce: 6 X1 + 6 X2 ≤ 1800 Flavor: 4 X1 + 2 X2 ≥ 500 Meat: 5 X1 + 1 X2 ≤ 700 Gourmet Chili: X 1 ≥ 0 Campfire Chili: X 2 ≥ 0

37. The table below shows a project's activities (A — E); their normal and crash durations; and their normal and crash costs. What is the benefit of crashing activity A? O Cost reduction of up to $6,000 O Time reduction of up to seven days O Time reduction of up to three days O Cost reduction of up to $16,000

Time reduction of up to three days cuz Maximum Time Reduction for A is 3

Decision Tree Example 1 - Start Times the State of Nature by the Probability

Times the State of Nature by the Probability e.g. Strong Sales x Probability $10 million x 0.75

Network Diagrams Example 4 - Part 1 Determine the total length of the critical path's missing by H. Critical Path is always the longest.

Total = 32 Weeks ABCIJ = 30 weeks ADEGJ = 28 weeks ADEFJ = 31 weeks So ABHIJ needs to be at least 32 weeks.

54. A small manufacturer of mountain bikes located in Denver, Colorado, buys tires from a supplier in China. There is a monthly demand of 200 tires. The cost of placing an order is $200 and the holding cost is $24 per tire per year. If the purchasing price is $45 per tire and the economic order quantity is used, what is the total annual inventory cost? O $4,800 O $108,000 O $2,400 O $112,800 O $110,400

Total Annual Inventory Cost: $112,800 Total inventory for the year = 200 x 12 = 2400 tires per year holding cost $2ea Tires cost $45ea (2400 x 2) + ( 2400 x 45) 4,800 + 108,000 = 112,800 total inventory cost. holding cost is $24 per tire per year so 24 / 12 = 2 $2 + $45 = $47ea and 47 x 200 x 12 = 112,800 To calculate the annual holding cost, divide the EOQ by 2 and then multiply the result by the holding cost.

19 A textile company is a manufacturer of fireproof uniforms in Mexico. The company is planning on opening operations in the United States and Canada, which requires a capacity expansion of 100%. The company has three alternatives: build a large plant, build a small plant or subcontract. There are two possible states of nature: a favorable market and a moderate market. If the future market is favorable, the payoffs are $13, $5, and $7 million for building a large plant, building a small plant, and subcontracting, respectively. Similarly, for a future moderate market, the payoffs are $2, $8, and S3 million for building a large plant, building a small plant, and subcontracting, respectively. The company has estimated the probability of a favorable market as 0.40. The textile company needs to make a decision about either building a plant or subcontracting. What is the relationship between uncertainty and the decision-making process in this scenario? O Uncertainty about a future moderate market makes the decision-making process unfeasible. O Uncertainty makes the decision-making process more difficult. O Uncertainty is less relevant to the decision-making process than risk. O Uncertainty is an inherent part of the decision-making process.

Uncertainty is less relevant to the decision-making process than risk. Key Differences Between Risk and Uncertainty. The risk is defined as the situation of winning or losing something worthy. Uncertainty is a condition where there is no knowledge about the future events. Speculation of uncertain events may lead to inaccurate decisions.

5 An employee working for the Highway Safety Department in Albany, New York has the job to predict the automobile accidents in Albany for the next year. The employee currently has monthly data on the following variables for the city of Albany: the number of automobiles registered, the sales of alcoholic beverages, and the rainfall in inches. How can this employee realistically predict the accidents in Albany for next year? O Use the ratio of accidents versus each of the other variables and then average the three values O Use a multiple regression equation using accident as the dependent variable and others as independent variables O Use a multiple regression equation using automobiles registered as the dependent variable and others as independent variables O Use the sales of alcoholic beverages because the other variables are less significant

Use a multiple regression equation using accident as the dependent variable and others as independent variables. cuz accidents the question, are the dependent variable the reason why is because rain, alcohol, distracted, etc.

24 A high school club has hosted an annual holiday craft fair for the last 10 years to raise money for the club. The craft fair has always been held in the high school gymnasium, but the gym is getting crowded as more crafters and shoppers attend the event each year. The club is considering four possible locations for this years fair. The table below shows the four alternatives, the probability for each type of weather during the event, and the estimated profits for each location and each type of weather. The cost for each location has already been factored into the table. Alternative 1. Stay in high school gymnasium 2. Use gym and covered walkway outside gym 3. Move to football field-open air event 4. Move to football field-use pavilions Rainy, Probability 10% 1. $ 3,500 2. $ 3,200 3. $ -100 4. $ -500 Sunny, Probability 60% 1. $ 5,000 2. $ 5,800 3. $ 6200 4. $ 6,000 Overcast, Probability 30% 1. $ 4,500 2. $ 3,200 3. $ 2,500 4. $ 3,500 If the expected value of each alternative is calculated, which scenario should the high school club invest in? O Move to football field — use pavilions O Move to football field — open air event O Stay in high school gymnasium O Use gym and covered walkway outside gym

Use gym and covered walkway outside gym cuz (3500x.1)+(5000x.6)+(4500x.3)=4700 and (3200x.1)+(5800x.6)+(3200x.3)=4760 and (-100x.1)+(6200x.6)+(2500x.3)=4460 and (-500x.1)+(6000x.6)+(3500x.3)=4600

23 Dawn owns a dog day care company that offers kenneling services for dogs that weigh less than 30 pounds. Dawn has decided to expand the building that houses the kennels by 1,000 square feet. She needs to decide whether to use the added square footage to continue only boarding dogs under 30 pounds or to start accommodating larger dogs. Dawn has estimated that if she allocates the expansion to larger dogs, she will earn additional revenue of $22,000 per year in a strong economy and additional revenue of $16,000 per year in a weak economy. If the expansion is exclusively for dogs under 30 pounds, she will earn additional revenue of $20,000 per year in a strong economy and additional revenue of $17,500 per year in a weak economy. She believes the likelihood of a strong economy is 60% and the likelihood of a weak economy is 40%. Which option provides the best payout for Dawn's business? O using the expansion for large dogs, with a payout of $19,600 O using the expansion for large dogs, with a payout of $19,000 O using the expansion for dogs under 30 pounds, with a payout of $19,000 O using the expansion for dogs under 30 pounds, with a payout of $18,500

Using the expansion for large dogs, with a payout of $19,600 Large (22,000 x 0.6)+(16,000 x 0.4) = 19,600, and Small (20,000 x 0.6)+(17,500 x 0.4) = 19,000

Network Diagrams Example 4 - Part 2 Determine the length of the critical path's missing value H. Critical Path is always the longest.

Value H = 12 Weeks Since A+B+I+J = 20 weeks and ABHIJ = 32 weeks, the minimum value for H needs to be 32 - 20 = 12 weeks.

Decision-Making Model Steps - Step 3

Weigh Decision Criteria (must equal 1 [100%])

Linear Programming Example 1 The West Coast Chili Company makes an expensive Gourmet Chili and a less expensive Campfire Chili, the rugged and rustic blend. They want to maximize profits while addressing the constraints to make these two brands of chili. Profits for the Gourmet Chili are $250 per batch while profits for the Campfire Chili are $150 per batch. We want to maximize profits. Using coordinates (100, 0) or (0, 166.667)

What is the objective function? Let X1 = the number of batches of Gourmet Chili and X2 = the number of batches of Campfire Chili Profit = Max Z = 250X1 + 150X2 . Max Z = 250X1 + 150X2 = 250 x 100 + 150 x 0 = 25000 + 0 = $25,000 (profit) [profit will be the same regardless of X or Y access] (MinZ = Minimum)

42. Consider the following linear programming formulation: Min Z = X1+X2 Subject to X1 + X2 ≥3 X1 + X2 ≥5 X1, X2 ≥0 Identify the feasible region in the graph below. Only one constraint will be shifted at a time. Which shift will produce an increase of the current feasible area? O X1 + X2≥3 shifts to X1 + X2≥4 O X1 + X2≥5 shifts to X1 + X2≥4 O X1 + X2≥5 shifts to X1 + X2≥6 O X1 + X2≥3 shifts to X1 + X2≥2 O X1 + X2≥3 shifts to X1 + X2≥5

X 1 + X 2 ≥ 5 shifts to X 1 + X 2 ≥ 4 cuz current feasible area is to the right of X2=(0,5) and X3=(5,0) x> is greater than 5 cuz constraint X1+X2≥5 supersedes all other constraints to add more area the line needs to move in to (0,0) shifting from ≥5 to ≥4 adds area

Ordering Cost The number of orders that occur annually can be found by dividing the annual demand by the volume per order. The formula can be expressed as:

number of Orders = D / Q D: Annual Quantity Demanded Q: Volume per Order

51. Total Inventory Value Based on the above diagram, what is the average inventory value for the year? Jan 300 + Feb 350 + Mar 350 + Apr 450 + May 450 + Jun 500 + Jul 500 + Aug 500 + Sep 600 + Oct 600 + Nov 550 + Dec 550 O € 400 O € 550 O € 475 O € 525

€ 475 cuz 300+350+350+450+450+500+500+500+600+600+550+550 = 5,700 / 12 = 475

Network Diagrams Example 1 (A) - Completed

𝑡 = (? + 4x? +??) -------------------- 6 A 6.00 6.50 10.00 Answer = 7.0 B 4.00 7.00 13.00 Answer = 7.50 C 9.00 13.25 22.00 Answer = 14.00 D 3.50 6.50 9.50 Answer = 6.50 E 1.00 6.00 8.00 Answer = 5.50 F 1.85 2.00 5.15 Answer = 2.50 G 1.00 5.00 9.00 Answer = 5.00 H 2.00 3.00 4.00 Answer = 3.00 I 1.00 4.00 4.00 Answer = 3.50 J 1.00 2.00 3.00 Answer = 2.00