MBA 515 Quizzes

Which constraint would insure there are at least three times as many X5's as X1's?

3X1 - X5 <= 0

Look at the following graph of a linear programming problem and answer the question below the graph:

A,B,C,E,G

Suppose your company uses a blend of 4 ingredients, X1, X2, X3, and X4 to make a special produce you sell. What would the constraint look like if you want to insure at least 30% of X2 ingredient will be in the final product?

.3X1 - .7X2 + .3X3 + .3X4 <= 0

Our company processes widgets. Consider the following data for 23 widgets in the file "Module 3 Quiz Widgets.xlsx". Each widget was weighed before and after processing. Use regression to test to see if the weight of a widget before processing is related to the weight of the widget after processing. If you are asked to predict how much a widget weighting .85 pounds will weight after processing what would you predict?

.4174

Consider the data file "Module 1 Quiz data.xlsx" in the "Module 1 Quiz" folder on our class LMS webpage. Construct an relative and relative frequency distribution for the data in column A for the tab "Q1". What is the absolute frequency of weights that are >200,000 but <=250,000?

183

Bullseye Shirt Company makes three types of shirts: athletic, varsity, and surfer. The shirts are made from different combinations of cotton and rayon. The cost per yard of cotton is $5 and the cost for rayon is $7. Bullseye can receive up to 4000 yards of cotton and 3000 yards of rayon per week. The table below shows relevant manufacturing information: Assume that the decision variables are defined as follows: Xij = yards of fabric i (C or R) blended into shirt j (A, V or S) where: A = athletic shirt, V = varsity shirt, S = surfer shirt, C = cotton, R = rayon The objective function for this linear programming problem would be: Max Profit = #30 [(XAC+ XAR) / 1.0] + $40 [(XVC + XVR) / 1.2] + $36 [(XSC + XSR) / .9] - $5 (XAC + XVC + XSC) - $7 (XAR + XVR + XSR) Note: The amount (XVC + XVR) / 1.2 would give you the number of Varsity shirts produced because the sum XVC + XVR is the total number of yards of material used in Varsity shirts and it takes 1.2 yards per shirt. So, if XVC + XVR = 2.4 then you would be producing 2 shirts. This constraint to insure there is no more than 30% Rayon in a Varsity shirt would be:

.30 (XVC + XVR) >= XVR

George is buying lunch for the Business Analytics faculty. There are 10 faculty members so he must buy exactly 10 sandwiches. He has three different sandwich specials to choose from: Turkey Delight, Ham-it-Up, and Roasted Beast. The Turkey Delight cost $4.5 and has 5 grams of fat and 200 calories, the Ham-it-Up costs $5 and has 4 grams of fat and 150 calories, and the Roasted Beast costs $6.5 and has 2 grams of fat and 100 calories. George would like no more than a total of 30 grams of fat for all 10 sandwiches. He was also like for the total amount of calories for all 10 sandwiches to be at least 1200 calories. Formulate a linear programming problem in Excel and use Solve to find the optimal solution. He would like to know how many of each sandwich special to buy to minimize costs. What should George buy?

0 Turkey Delight, 5 Ham-it-Up, and 5 Roasted Beast

Consider the data file "Module 2 Quiz Account Information.xlsx" in the "Module 2 Quiz" folder on our class LMS page. Construct a pivot table to show the number of accounts by balance due and number of days overdue like the following table: How many accounts have a balance in the row 3000-3999 and in the column 40-49 days overdue?

1

Wright-Rentals rents boats on a daily basis. Currently they have zero boats and need to establish their fleet for the next season. They have three basic types of boats they can purchase: sail boats, ski boats, and party boats. They have three constraints they must deal with each day. They only have 48 labor hours (8 workers at 6 hr./worker) available for cleaning boats when they are returned at night. They only have 100 minutes of setup time each morning (2 workers at 50min./worker). There is also only 400 square feet of storage space available in their yard. The resource requirements per day and the rental profit per day for each type of boat is as follows: Notice there is no setup time for sail boats because they do not have motors that must be fueled and maintained. Wright-Rentals believes they can rent all the boats they have available every day. Formulate and solve a linear program to determine how many of each type boat Wright-Rentals should purchase to maximize their rental profits. If solver gives you a non-integer solution for a boat type that is OK for this question! For instance solver could find 2.5 ski boats as optimal and that would be the correct answer to this question.

1,375

Suppose you know the optimal solution for a 2 decision variable linear programming problem in at the intersection of the following 2 constraints: 10 X1 + 5 X2 = 70 and 20 X1 + 80 X2 = 840 What is the value of X2 at this optimal solution point?

10

Wright-Rentals rents boats on a daily basis. Currently they have zero boats and need to establish their fleet for the next season. They have three basic types of boats they can purchase: sail boats, ski boats, and party boats. They have three constraints they must deal with each day. They only have 48 labor hours (8 workers at 6 hr./worker) available for cleaning boats when they are returned at night. They only have 100 minutes of setup time each morning (2 workers at 50min./worker). There is also only 400 square feet of storage space available in their yard. The resource requirements per day and the rental profit per day for each type of boat is as follows: Notice there is no setup time for sail boats because they do not have motors that must be fueled and maintained. Wright-Rentals believes they can rent all the boats they have available every day. Formulate and solve a linear program to determine how many of each type boat Wright-Rentals should purchase to maximize their rental profits. Suppose management wanted to insure at least one of each type of boat is purchased. How much would it cost Wright-Rentals to add this constraint?

15

Consider the data file "Module 1 Quiz data.xlsx" in the "Module 1 Quiz" folder on our class LMS page. Consider the data on the Q3 tab. Determine the lower and upper fences to use for a box plot of this data by using: Lower fence: Q1 - (1.5 * IQR) Upper fence: Q3 + (1.5 * IQR) How many of the values in the data are less than the lower fence?

18

Consider the data file "Module 1 Quiz data.xlsx" in the "Module 1 Quiz" folder on our class LMS page. Consider the data on the Q9 tab. Count the number of rows with either a Balance Due over 4000 or a Days overdue > 40. What is the count?

238

Consider the "Module 3 Quiz Restaurant Tips.JMP" file. Use "Analyze/Fit Model" in JMP to build a multiple regression model with Tip Amount as the Y variable and Bill Amount, Number of Guests, and Server as the independent variables (called "Model Effects in JMP). Run this model in JMP. Go to the results window in JMP and click on the red chevron beside "Response Tip Amount" and select "Save Columns/Save Prediction Formula" (below is a screen shot of how to do this): You have now saved a new column with the prediction of Tip Amount for each row based on the model JMP created. Go back to your data and page down to the bottom of the data and create a new row with: a bill of $25, 3 guests, and server B What is the predicted tip amount (in the predicted column) for this row?

3.83

Consider the data file "Module 1 Quiz data.xlsx" in the "Module 1 Quiz" folder on our class LMS page. Consider the data on the Q5 tab. Use the grading scale in D2:E14 to determine a letter grade for each of the 500 scores. How many rows have a grade of A-? (Hint: use VLOOKUP)

40

Consider the data file "Module 1 Quiz data.xlsx" in the "Module 1 Quiz" folder on our class LMS page. Consider the data on the Q2 tab and assume this data is from a sample. What is the median for this data?

42

Consider the data file "Module 2 Quiz Titantic.xlsx" in the "Module 2 Quiz" folder on our class LMS page. Create a pivot table in Excel for this data. Add "Sex" to the column area, "Survived" and "Fare" to the Row area. Put a count of "Sex" in the Values area. Use a range for the rows and columns exactly like the table below: Based on this pivot table how many Females paid a fare of AT LEAST 100 and survived (you will need to sum the counts of all ranges from 100-150 to 250-300)?

48

Consider the data file "Module 1 Quiz data.xlsx" in the "Module 1 Quiz" folder on our class LMS page. Consider the data on the Q4 tab. The data for your analysis is in columns B through Z. How many cells in column T are missing a value? Count all blank cells ("") and all cells with spaces (" ") in your total. Hint: use the =CountIF() function

5

Bullseye Shirt Company makes three types of shirts: athletic, varsity, and surfer. The shirts are made from different combinations of cotton and rayon. The cost per yard of cotton is $5 and the cost for rayon is $7. Bullseye can receive up to 4000 yards of cotton and 3000 yards of rayon per week. The table below shows relevant manufacturing information: Assume that the decision variables are defined as follows: Xij = yards of fabric i (C or R) blended into shirt j (A, V or S) where: A = athletic shirt, V = varsity shirt, S = surfer shirt, C = cotton, R = rayon The objective function for this linear programming problem would be: Max Profit = #30 [(XAC+ XAR) / 1.0] + $40 [(XVC + XVR) / 1.2] + $36 [(XSC + XSR) / .9] - $5 (XAC + XVC + XSC) - $7 (XAR + XVR + XSR) Note: The amount (XVC + XVR) / 1.2 would give you the number of Varsity shirts produced because the sum XVC + XVR is the total number of yards of material used in Varsity shirts and it takes 1.2 yards per shirt. So, if XVC + XVR = 2.4 then you would be producing 2 shirts. If the optimal solution has: XVC = 400, XVR = 260 The total number of Varsity shirts would be

550

Consider the data file "Module 1 Quiz data.xlsx" in the "Module 1 Quiz" folder on our class LMS page. Consider the data on the Q7 tab. This data is for 200 customers who visited our company webpage. Consider the Inquires column. You need to replace all missing values in this column. You have set up the following guideline to determine a value for Inquires: If Duration < 95 then the number of Inquires equals 50 If Duration >= 95 and <150 then the number of Inquires equals 100 If Duration >=150 then the number of Inquires equals 125 Apply these rules to the missing values in the Inquires column (cells with a "-"). What is the average number of Inquires for all 200 rows? Your answer needs to be correct to 2 decimal places! For instance, if you get 16.753 then 16.75 would be the correct answer. *Hint: If you use the Substitute function and get a column that looks like numbers but Excel doesn't recognize the values as numbers (you can't get an average) then use the function =NUMBERVALUE() to convert the column to a column with numbers that Excel will recognize as numbers.

81.25

Consider the data file "Module 1 Quiz data.xlsx" in the "Module 1 Quiz" folder on our class LMS page. Consider the data on the Q6 tab. What is the correct formula to use in cell G2 if you want "Didn't Purchase" to show in G2 unless the customer is either a female or has a Class (column A) of "1", in which case you would then want "Purchase" to show in G2?

=IF(OR(A2=1,D2="female"),"Purchase","Didn't Purchase")

Consider the data file "Module 1 Quiz data.xlsx" in the "Module 1 Quiz" folder on our class LMS page. Consider the data on the Q8a and Q8b tabs. Insert a new column in the Q8a worksheet just after column A (so columns B-F will now be columns C-G and there will be an empty column B). What would be the Excel code for cell B2 to match up the first customer's ID and bring the Name for this customer from the "Q8b" worksheet into "Q8a" worksheet? The formula MUST be correct with relative and absolute references that would allow you to copy this formula down the entire B Column so each customer will have the correct name. Notice the ID's in column A on worksheet Q8b are NOT in ascending order. Leave them this way.

=VLOOKUP(A2,Q8b!$A$2:$G$51,2,FALSE)

What is true about Data Visualizations?

A data visualization is any visual (not a math formula) tool that helps to understand the "story of the data". Data visualizations can help see patterns, trends, and correlations in the data that can be hidden in mathematical summaries.

Look at the following graph of a linear programming problem and answer the question below the graph: If we could produce X1 = 12.50 and X2 = 11.25 at point D we would have more profit than the optimal solution to this problem. What is preventing us from producing these values for X1 and X2?

Constraint #2 is preventing this solution from being feasible.

Consider the file "Module 2 Quiz Ads.xlsx" in the "Module 2 Quiz" folder. This file has the amounts spent on TV ads, Radio Ads, and the number of units sold for 450 days. Import this data into JMP Pro. Look at the box plots in the distributions for only TV Ads and Units Sold. Exclude and Hide all rows with TV Ads less than 140. Redo the distributions (without the rows for TV Ads < 140). Look for a relationship between TV ads and Units Sold based on these distributions. What do you see?

It seems TV Ads and Units sold are somewhat related in the following ways: 1) When less is spent on TV Ads the number of units sold are slightly lower. 2) When more is spent on TV Ads the number of units sold are slightly higher.

Bullseye Shirt Company makes three types of shirts: athletic, varsity, and surfer. The shirts are made from different combinations of cotton and rayon. The cost per yard of cotton is $5 and the cost for rayon is $7. Bullseye can receive up to 4000 yards of cotton and 3000 yards of rayon per week. Assume that the decision variables are defined as follows: Xij = yards of fabric i (C or R) blended into shirt j (A, V or S) where: A = athletic shirt, V = varsity shirt, S = surfer shirt, C = cotton, R = rayon The objective function for this linear programming problem would be: Max Profit = $30 [(XAC+ XAR) / 1.0] + $40 [(XVC + XVR) / 1.2] + $36 [(XSC + XSR) / .9] - $5 (XAC + XVC + XSC) - $7 (XAR + XVR + XSR) Note: The amount (XVC + XVR) / 1.2 would give you the number of Varsity shirts produced because the sum XVC + XVR is the total number of yards of material used in Varsity shirts and it takes 1.2 yards per shirt. So, if XVC + XVR = 2.4 then you would be producing 2 shirts. This objective function can be described as

Maximizing Profits from all shirts produced. Where profit is revenue minus cost for each shirt type. The revenue for a type of shirt is the number of shirts produced multiplied by the selling price for for that shirt type. The cost for a shirt type is the sum of the costs of both materials used in a shirt type (NOT multiplied by the number of shirts).

Unused resources in a linear programming problem are referred to as Slack or Surplus depending on the type of constraint. Slack is when you do not use all of an available resource. An example of slack would be when there are 40 hours of labor available but the optimal solution only uses 38 hours of labor. Surplus is when you use more of a resource that is necessary. An example would be when a model requires a minimum of 200 mg of vitamin A and the optimal solution has 300 mg of vitamin A. Would an objective function that minimizing the slack and surplus for your constraints be the same as an objective function that maximizing profits or minimizing costs?

No, You could get a different optimal solution

The major difference between Predictive Analytics and Prescriptive Analytics is

Predictive Analytics deals with making decisions based on probabilities while Prescriptive Analytics deals with making decisions that are complicated but have no probabilities to deal with.

Suppose you produce two new types of smart phones, a Walkman and a Watch-TV. For each Walkman phone you produce you make a profit of $10 (instead of $7 as in the previous problem) and for each Watch-TV phone you produce you make $5. There are two constraints preventing you from making an infinite number of phones. An electronics constraint and an assembly constraint. The Linear Programming formulation for this problem is: Let X1 = the number of Walkmans to be producedLet X2 = the number of Watch-TVs to be produced Maximizeprofit=10X1+5X2 subject to: 4X1+3X2≤240(electronicconstraint) 2X1+X2≤100(assemblyconstraint) X1≥0,X2≥0(non−negativity) Here is the feasible solution space for this problem:

Produce EITHER zero Watch -TV's and 50 Walkmans OR 40 Watch -TV's and 30 Walkmans. Both of these are optimal and there are an infinite number of optimal solutions "between" these two points on the binding constraint line (the Assembly constraint).

Consider worksheet "ws1" in file "Module 3 quiz Sales.XLSX". Construct 3 different simple linear regression models where Sales is the dependent variable in each model and the independent variables are TV Ads, Newspaper Ads, and Radio Ads respectively. Look at and remember the P-values for each of the three models. Construct a new multiple linear regression model with all three independent variables (TV, Newspaper, and Radio Ads) and Sales as the dependent variable. You should now know three things: 1) the P-values of each independent variable in 3 separate simple linear regression models 2) the P-value of the full multiple regression model with 3 independent variables (this is only 1 model with 3 independent variables). 3) the P-values within the multiple regression model for each of the independent variables (from the one multiple regression model). How do you explain what you see from these three results?

The P-value for the "Full" multiple regression model is smaller than the common significance level threshold of .05. This indicates there is sufficient evidence of a significant relationship between (at least one of) the independent variables (TV, Newspaper, Radio ads) and the dependent variable (Sales). However, in the results of the multiple regression model the individual p-values for each of the three independent variables are NOT significant (they are all much larger than .05). This contradicts what the individual simple linear regression models showed for some of the independent variables. Therefore, there must be something going on between the independent variables in the multiple regression model because the P-values for the independent variables in the multiple regression model are misleading.

Open the JMP software. Open the file "Module 2 Quiz Boston Housing.jmp". Each row is for an area around Boston. The "mvalue" variable is the median value of a home in that area. The "age" variable is the proportion of homes in the area built prior to 1940. Use the Analyze/Distributions option to look at the distributions for the two variables "age" and "mvalue". What would you say about the relationship between areas with at least 80% of homes built prior to 1940 and the median value of homes in the area?

The areas with at least 80% of homes built prior to 1940 have lower median values compared to homes in areas with less than 80% of homes built prior to 1940.

What is meant by "Independent variable" (as opposed to Dependent variable) in regression analysis?

The independent variable is the "X" variable we have some control over. Some other names for the independent variable are predictor, regressor, model effect (in JMP)

Consider the data file "Module 2 Quiz Lost Sales.JMP" in the "Descriptive Analytics Test" folder on our class LMS page. Open this file in JMP Pro. Use the "Graph Builder" in JMP to look at Box Plots for Time to Delivery for both Won and Lost Status. Hint: put "Status" on the left side of the graph (in the Y area of the picture below) and "Time to Delivery" on the bottom (in the X area at the bottom of the picture below, NOT in the Group X area at the top). Looking at your box plots, what do you see for Won and Lost respectively?

There is more dispersion in the Lost data than the Won data.

Open the JMP software. Import the MS Excel file "Module 2 Quiz Titantic.xlsx" to JMP. In JMP, use graph builder to look at a scatter plot of fare, and passenger class. Put Passenger Class in the horizontal axis (bottom) and fare on the vertical Y axis (left). Click on the scatter plot points graph and the Line of fit graph: Which of the following choices best describes what you see?

There is much more dispersion in fares for first class passengers compared to the dispersion of fares for either the second or third class passengers.

Consider worksheet "ws1" in the file "Module 3 Sales.xlsx". Construct three separate simple linear regression models with each of the three types of advertising (TV, Newspaper, and Radio) expenditures as the independent variables and sales as the dependent variable in each model. What did you find from these models?

There is sufficient evidence of a positive relationship between Sales and expenditures on Newspaper Ads. There is also sufficient evidence of a positive relationship between Sales and expenditures on Radio Ads. However there is not significant evidence of any relationship between sales and expenditures on TV Advertising.

Consider the "Module 3 Quiz Restaurant Tips.JMP" file. Use "Analyze/Fit Model" in JMP to build a multiple regression model with Tip Amount as the Y variable and Bill Amount, Number of Guests, and Server as the independent variables (called "Model Effects in JMP). Run this model in JMP. Go to the results window in JMP and click on the red chevron beside "Response Tip Amount" and select "Save Columns/Save Prediction Formula" (below is a screen shot of how to do this): You have now saved a new column with the prediction of Tip Amount for each row based on the model JMP created. Go back to your data and page down to the bottom of the data and create a new row with: a bill of $100, 10 guests, and server B What is the predicted tip amount (in the predicted column) for this row?

These amounts are out of the range of my sample data so I would not use my model to predict the tip amount.

When would it be impossible to solve a linear programming problem using the two dimensional graphical technique you learning in this module?

When there are more than 2 deicison variables.

Look at the following graph of a linear programming problem and answer the question below the graph: If the objective function is Max Profit = 60X1 + 200X2 what is the optimal solution for X1 and X2? Correct!

X1 = 6, X2 = 8

Our company processes widgets. Consider the following data for 23 widgets in the file "Module 3 Quiz Widgets.xlsx". Each widget was weighed before and after processing. Test to see if the weight of a widget before processing is related to the weight of the widget after processing. Are the two measurements related? Why did you make this conclusion?

Yes, the two columns are positively related because the estimated value of β1 is positive (.5414) and the P-value for the test is .0002.

Consider the "Module 3 Quiz Restaurant Tips.JMP" file. Use "Analyze/Fit Model" in JMP to build a multiple regression model with Tip Amount as the Y variable and Bill Amount, Number of Guests, and Server as the independent variables (called "Model Effects in JMP). Run this model in JMP. You should see this in the results: This table shows a P-value of <.0001 for the multiple regression model. What does that tell you?

You have a "good" model that can be used to predict the amount of tip a server will receive if you know the value of each of the independent variables and the values of the independent variables are withing the range of the sample data used to construct the model.

A linear programming models cannot have more than 2 decision variables otherwise you would not be able to find an optimal decision.

false

It would be impossible to have a common feasible solution space if a 2 decision variable linear programming model had both <= and >= constraints.

false

You could find the optimal solution graphically for any linear programming problem with 2 decision variables even if you do not know what the objective function is (all you need to know is the feasible solution space and all the corner points of the feasible solution space.

false

Regression analysis was applied and a significant relationship between product demand (Y) and the product price (X) was found. The following estimated regression equation was obtained.Yhat = 120 + 10 XBased on the above estimated regression equation, if price is increased by 2 units, then demand is expected to

increase by 20 units

Suppose you produce two new types of smart phones, a Walkman and a Watch-TV. For each Walkman phone you produce you make a profit of $7 and for each Watch-TV phone you produce you make $5. There are two constraints preventing you from making an infinite number of phones. An electronics constraint and an assembly constraint. The Linear Programming formulation for this problem is: Here is the feasible solution space for this problem: Management just gave you a new requirement. The Walkman phones are really selling well so they want to be sure they produce exactly twice as many Walkmans as Watch-TV phones. What is the optimal number of each type to produce to meet all requirement now?

none

In regression analysis the parameter β1 is a Population Parameter measuring

the slope of the Population regression line computed from a census of the Population

Consider the file "Module 2 Quiz Ads.xlsx" in the "Module 2 Homework" folder. This file has the amounts spent on TV ads, Radio Ads, and the number of units sold for 450 days. Import this data into JMP Pro. Look at the box plot in the distribution for radio ads. There is one possible outlier for radio ads but it is most likely an OK data point to use because it is so close to the lower fence and looks to be typically for this distribution.

true

You cannot solve a linear programming model graphically if there are 4 decision variables in the model.

true