Quantitate methods of business test 1

A university is planning a seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even?

$175

Cully Furniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the maximum profit?

$45,000

The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B, which cost 50 cents and 75 cents per pound, respectively. Five essential ingredients are contained in the feed, shown in the table below. The table also shows the minimum daily requirements of each ingredient.

.3b>/ 20

Assume that x2, x7 and x8 are the dollars invested in three different common stocks from New York stock exchange. In order to diversify the investments, the investing company requires that no more than 60% of the dollars invested can be in "stock two". The constraint for this requirement can be written as:

.4x2 - .6x7 - .6x8</ 0

Quickbrush Paint Company is developing a linear program to determine the optimal quantities of ingredient A and ingredient B to blend together to make oil-base and water-base paint. The oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. Assuming that x represents the number of gallons of oil-base paint, and y represents the gallons of water-base paint, which constraint is correctly represents the constraint on ingredient A?

.9x + .3y </ 10,000

The owner of Chips etc. produces two kinds of chips: Lime (L) and Vinegar (V). He has a limited amount of the 3 ingredients used to produce these chips available for his next production run: 4800 oz of salt, 9600 oz of flour, and 200 oz of herbs. A bag of lime chips require 2 oz of salt, 6 oz of flour, 1 oz of herb to produce, while a bag of vinegar chips requires 3 oz of salt, 8 oz of flour, and 2 oz of herb. which of the following is NOT feasible

0l and 1200v

the optimal quantity of the 3 products and resulting revenue for taco loco is

1.45z 8.36y 0z for 129.09

given the following linear program that maximizes revenue: max z= 15x + 20y 8x + 5y</ 40 4x + y >/4

160

what is the range in values for beef inventory that would not affect the optimal product mix

17.78 to 30 pounds

Administrators at a university will charge students $150 to attend a seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per student for the administrators to provide the course materials. How many students would have to register for the seminar for the university to break even?

24

how many pounds of beans will taco loco have left over if they produce the optimal quantity of products x y z

28.73

The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular (R) and diet(D). Two of the limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint?

2R + 4D ≤ 480

The owner of Chips etc. produces two kinds of chips: Lime (L) and Vinegar (V). He has a limited amount of the 3 ingredients used to produce these chips available for his next production run: 4800 oz of salt, 9600 oz of flour, and 200 oz of herbs. A bag of lime chips require 2 oz of salt, 6 oz of flour, 1 oz of herb to produce, while a bag of vinegar chips requires 3 oz of salt, 8 oz of flour, and 2 oz of herb. constraint for salt ?

2l+ 3v</ 4800

Belmont has bids from two companies to build it's new indoor sports facility. It will choose between Company A and Company B. Company A has a fixed cost of 75,000 and a variable cost of 15. Company B's fixed cost is 90,000 and variable cost is 11. Use the total cost equation for each company and compare them. At what volume is the total cost the same, that is at what volume is Belmont indifferent between the two bidders?

3,750

Atwitter The college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean. The communications director's market research revealed the following: Medium Exposure Cost Newspaper 5,000 $500 Radio 3,000 $250 Twitter 700 $25 Facebook 200 $15 The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140 character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.) how many potential customers will be reached by the optimal advertising campaign?

42,080

The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. The equation for constraint DH is:

4X + 8Y ≥ 32.

AtwitterThe college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean.The communications director's market research revealed the following:Medium Exposure CostNewspaper 5,000 $500Radio 3,000 $250Twitter 700 $25Facebook 200 $15The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140 character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.)Which of these is an appropriate constraint for this scenario?

500N + 250R + 125T + 15F ≤ 3,500

Which of the following statements about infeasible problems is best?

All of the possible solutions violate at least one constraint

Cully Furniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. In order to maximize profit, how many big shelves (B) and how many medium shelves (M) should be purchased?

B = 150, M = 0

The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. Which line is represented by the equation 2X + Y ≥ 8?

BF

The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. Which of the following constraints has a surplus greater than 0?

DH

________ are generally independent of the volume of units produced and sold

Fixed costs

The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. Which of the following points is not feasible?

G

In a linear programming problem, a valid objective function can be represented as:

Max Z = 3 x + 3 y + 1/3 z

AtwitterThe college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean.The communications director's market research revealed the following:Medium Exposure CostNewspaper 5,000 $500Radio 3,000 $250Twitter 700 $25Facebook 200 $15The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140 character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.)What is an appropriate objective function for this scenario?

Max Z = 5,000N + 3,000R + 700T + 200F

The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What are the optimal daily production quantities of each product and the optimal daily profit?

R = 90, D = 75, Z = $420

A hot dog manufacturer wishes to minimize the cost in dollars of producing a low-cost niched product while meeting the dietary guidelines for protein and sodium. Once the model has been run, the surplus variable in the sodium constraint has a value of 1300 milligrams. The best interpretation of this outcome is:

The minimum cost hot dog has 1300 milligrams more sodium than required.

Which of the following is an equation or an inequality that expresses a resource restriction in a mathematical model?

a constraint

In the formulation of a ≥ constraint:

a surplus variable is subtracted

in a multi period scheduling problem, the production constraint usually takes the form of

beginning inventory- demand+ production+ ending inventory

The indicator that results in total revenues being equal to total cost is called the:

break-even point.

the local cheese vendor offers to sell taco loco 200 pounds of cheese for these 3 products. they should

buy 46 pounds or less of cheese for $1.45 or less

If fixed costs decrease, but variable cost and price remain the same, the break-even point:

decreases.

If the price increases, but fixed and variable costs do not change, the break-even point:

decreases.

A model is a functional relationship that includes:

equations. variables. parameters.

The region that satisfies all of the constraints in a graphical linear programming problem is called the:

feasible solution space.

Atwitter The college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean. The communications director's market research revealed the following: Medium Exposure Cost Newspaper 5,000 $500 Radio 3,000 $250 Twitter 700 $25 Facebook 200 $15 The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140 character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.) how should the reduced cost entry for the newspaper decision variable be interpreted?

if the director were forced to purchase advertisement, he would reach 1000 fewer customers than would be reached using the optimal advertising campaign

for a maximum problem, the shadow price measures the ____ in the value of the optimal solution ____.

improvement, resource

The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. The constraint AJ

is a binding constraint.

A slack variable:

is the amount by which the left side of a ≤ constraint is smaller than the right side.

The optimal solution to a linear programming model that has been solved using the graphical approach:

is typically at some corner of the feasible region.

The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. This linear programming problem is a(n):

minimization problem.

The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. For the production combination of 135 cases of regular and 0 cases of diet soft drink, which resources will not be completely used?

only time

sensitivity analysis is the analysis of the effect of ___ changes on the ___

parameter, optimal solution

The purpose of break-even analysis is to determine the number of units of a product to sell that will:

result in zero profit.

The owner of Chips etc. produces two kinds of chips: Lime (L) and Vinegar (V). He has a limited amount of the 3 ingredients used to produce these chips available for his next production run: 4800 oz of salt, 9600 oz of flour, and 200 oz of herbs. A bag of lime chips require 2 oz of salt, 6 oz of flour, 1 oz of herb to produce, while a bag of vinegar chips requires 3 oz of salt, 8 oz of flour, and 2 oz of herb.

salt only

For a maximization problem, assume that a constraint is binding. if the original amount of a resource is 4lbs. and the range o feasibility for this constraint is from 3lbs to 6lbs,increasing the amount of this resource by 1lbs will result in

same product mix, different total profit

Variable cost does not include:

staff and management salaries.

A shadow price reflects which of the following in a maximization problem?

the marginal gain in the objective that would be realized by adding one unit of a resource

Atwitter The college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean. The communications director's market research revealed the following: Medium Exposure Cost Newspaper 5,000 $500 Radio 3,000 $250 Twitter 700 $25 Facebook 200 $15 The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140 character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.) which of these statments about the sensitivity report for the constraints is best?

the marginal value is 12 for every additional unit of budget

At the break-even point:

total revenue equals total cost.

The production manager for Beer etc. produces two kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. The manager can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week, respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. Which of the following is not a feasible solution?

wheat only 300l and 200d 800

For a linear programming problem, assume that a given resource has not been fully used. We can conclude that the shadow price associated with that constraint:

will have a value of zero

For a resource constraint, either its slack value must be ________ or its shadow price must be ________.

zero, zero