It is important to understand the assumptions underlying the use of any quantitative analysis model. What are the assumptions and requirements for an LP model to be formulated and used? 1. 2. What are the components of defining a problem in Excel so that it can be solved using Solver 3. Explain why knowing how to use Excel to set up and solve LP problems may be beneficial to a manager. 4. How is slack (or surplus) calculated for a constraint? How is it interpret

It is important to understand the assumptions underlying the use of any quantitative analysis model. What are the assumptions and requirements for an LP model to be formulated and used? 1. 2. What are the components of defining a problem in Excel so that it can be solved using Solver 3. Explain why knowing how to use Excel to set up and solve LP problems may be beneficial to a manager. 4. How is slack (or surplus) calculated for a constraint? How is it interpret

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter8: Evolutionary Solver: An Alternative Optimization Procedure

Section: Chapter Questions

Problem 35P

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Chapter 6. Solve the following Linear Program using the Solver method and answer the questions given below (round to two decimal places): Maximize 12A + 15B s.t. 3A + 7B <= 250 5A + 2B <= 200 B <= 25 A, B >= 0 a. The optimal value of A is 31.03 and the optimal value of B is 22.41. b. The maximized function yields a solution of 708.62. Chapter 7. For the problem you solved in Q1, obtain the Sensitivity Report, and answer the following questions. Remember to round to two digits and you can enter “infinity” for unlimited regions: The range for Variable A is from ????? to ????? The range for Variable B is from ????? to ????? The range for Constraint 1 is from ????? to ????? The range for Constraint 2 is from ????? to ????? The range for Constraint 3 is from ????? to ?????
This exercise is based on the following data on four bodybuilding supplements. (Figures shown correspond to a single serving.) Creatine(grams) L-Glutamine(grams) BCAAs(grams) Cost($) Xtend(SciVation) 0 2.5 7 1.00 Gainz(MP Hardcore) 2 3 6 1.10 Strongevity(Bill Phillips) 2.5 1 0 1.20 Muscle Physique(EAS) 2 2 0 1.00 Your personal trainer suggests that you supplement with at least 5 grams of creatine, 35.5 grams of L-glutamine, and 85 grams of BCAAs each week. You are thinking of combining Xtend and Gainz to provide you with the required nutrients. How many servings of each should you combine to obtain a week's supply that meets your trainer's specifications at the least cost? (If an answer does not exist, enter DNE.) servings of xtend = ___ servings of gainz = ___
DynaTune is trying to determine how to allocate its $145,000advertising budget for a new product. Radio and television arethe two media outlets selected for advertising. Th e followingtable shows the costs of advertising in these two media and theestimated number of new customers reached by increasingamounts of advertising For example, each of the fi rst 10 ads the company places on theradio will cost $1000 and is expected to reach 900 new customers.Each of the next 10 will cost $900 and is expected to reach 700new customers. Assume the company will purchase no more than30 radio ads and no more than 15 television ads.(a) Formulate an LP to maximize the number of newcustomers reached.(b) Set up and solve the problem on a spreadsheet.(c) What is the optimal solution? Explain the rationale for thesolution.(d) Suppose the number of new customers reached by 11–15television ads is 7500 and the number reached by 6–10ads is 5000. Resolve the problem. What is wrong with thissolution? Is Solver…
This exercise is based on the following data on four bodybuilding supplements. (Figures shown correspond to a single serving.) Creatine (grams) L-Glutamine (grams) BCAAs (grams) Xtend(SciVation) 0 2.5 7 Gainz(MP Hardcore) 2 3 6 Strongevity(Bill Phillips) 2.5 1 0 Muscle Physique(EAS) 2 2 0 Your personal trainer suggests that you supplement with as much BCAAs as possible but with no more than 36 grams of creatine and 54 grams of L-glutamine per week. You are thinking of combining Xtend, Gainz, and Strongevity to provide you with the required nutrients. How many servings of each should you combine to obtain a week's supply that meets your trainer's specifications and also includes at least as many servings of Strongevity as Xtend? Xtend servings Gainz servings Strongevity servings How much BCAAs will you obtain? g
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Based on Brams and Taylor (2000). Suppose that EliLilly and Pfizer are going to merge. Merger negotiations must settle the following issues: ■ What will the name of the merged corporation be?■ Will corporate headquarters be in Indianapolis(Lilly wants this) or New York (Pfizer wants this)?■ Which company’s chairperson will be chairperson of the merged corporation?■ Which company gets to choose the CEO?■ On the issue of layoffs, what percentage of each company’s view will prevail?Brams developed a remarkably simple method for the two adversaries to settle their differences. (This same method could be used to settle differences between other adversaries, such as a husband and wife in a divorce, Arab and Israel in Middle East, and so on.) Each adversary allocates 100 points between all of the issues. These allocations are listed in the file P04_84.xlsx. For example, Lilly believes headquarters is worth 30 points, whereas Pfizer thinks headquarters is worth only 15 points. Layoffs may be…
The board of directors of General Wheels Company is considering seven large capital investments. Each investment can be made only once. These investments differ in the estimated long-run profit (net present value) that they will generate as well as in the amount of capital required, as shown by the following table. Investment Opportunity 1 2 3 4 5 6 7 Estimated Profit ($million) 17 10 15 19 7 13 9 Capital Required for Investment Opportunity ($million) Capital Available ($million) 1 2 3 4 5 6 7 Capital 43 28 34 48 17 32 23 100 The total amount of capital available for these investments is $100 million. Investment opportunities 1 and 2 are mutually exclusive, and so are 3 and 4. Furthermore, neither 3 nor 4 can be undertaken unless one of the first two opportunities is undertaken. There are no such restrictions on investment opportunities 5, 6, and 7. The objective is to select the combination of capital investments that will maximize the total estimated long-run…
I NEED HELP WITH QUESTION D AND E. Adirondack Savings Bank (ASB) has $1,000,000 in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 7% for home loans, 12% for personal loans, and 9% for automobile loans. The bank's planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans. a. Formulate a linear programming model that can be used to determine the amount of funds ASB should allocate to each type of loan in order to maximize the total annual return for the new funds. b. How much should be allocated to each type of loan? What is the total annual return? What is the annual percentage return? c. If the interest rate on home loans increased to 9%, would the amount allocated to each type of loan…
BIG produces four types of yogurts A, B, C, and D. Each box of yogurt carries protein, sugar, and Fat. The following table provides information about content of each box of yogurt together with production cost of each box. Protein /Box Sugar/Box Fat/Box Production Cost/Box Yogurt A 10 3 1.5 $ 2.00 Yogurt B 20 2 1 $ 3.00 Yogurt C 30 2.5 1.5 $ 5.00 Yogurt D 20 2 1.5 $ 3.50 BIG wants to produce yogurts in such a way that will provide at least 400 grams of protein with minimum production cost. However, BIG also have to make sure they are not providing more than 200 gm of Sugar and 200 gm of Fat while providing the required protein. Moreover, BIG has to produce at least one unit of each type of yogurt and the number of yogurt A produced should not be more than the number of yogurt C produced. SOLVE USING EXCEL SOLVER
Shoemakers of America forecasts the following demandfor each of the next six months: month 1—5,000 pairs;month 2—6,000 pairs; month 3—5,000 pairs; month 4—9,000 pairs; month 5—6,000 pairs; month 6—5,000 pairs. Ittakes a shoemaker 15 minutes to produce a pair of shoes.Each shoemaker works 150 hours per month plus up to 40hours per month of overtime. A shoemaker is paid a regularsalary of $2,000 per month plus $50 per hour for overtime.At the beginning of each month, Shoemakers can either hireor fire workers. It costs the company $1,500 to hire a workerand $1,900 to fire a worker. The monthly holding cost perpair of shoes is 3% of the cost of producing a pair of shoeswith regular-time labor. (The raw materials in a pair of shoescost $10.) Formulate an LP that minimizes the cost ofmeeting (on time) the demands of the next six months. Atthe beginning of month 1, Shoemakers has 13 workers
Shoemakers of America forecasts the following demandfor each of the next six months: month 1—5,000 pairs;month 2—6,000 pairs; month 3—5,000 pairs; month 4—9,000 pairs; month 5—6,000 pairs; month 6—5,000 pairs. Ittakes a shoemaker 15 minutes to produce a pair of shoes.Each shoemaker works 150 hours per month plus up to 40hours per month of overtime. A shoemaker is paid a regularsalary of $2,000 per month plus $50 per hour for overtime.At the beginning of each month, Shoemakers can either hireor fire workers. It costs the company $1,500 to hire a workerand $1,900 to fire a worker. The monthly holding cost perpair of shoes is 3% of the cost of producing a pair of shoeswith regular-time labor. (The raw materials in a pair of shoescost $10.) Formulate an LP that minimizes the cost of At the conclusion of the season, this method has beenused to determine ratings for college football and collegebasketball. What problems could be foreseen if this methodwere used to rate teams early in the…
Consider the following linear program: MAX 3x1 + 4x2 ($ Profit) s.t. x1 + 3x2 £ 12 2x1 + x 2 £ 8 x1 £ 3 x1, x2 ³ 0 The Management Scientist provided the following solution output:OPTIMAL SOLUTIONObjective Function Value = 20.000 Variable Value Reduced Cost X1 2.400 0.000 X2 3.200 0.000 Constraint Slack/Surplus Dual Price 1 0.000 1.000 2 0.000 1.000 3 0.600 0.000 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit X1 1.333 3.000 8.000 X2 1.500 4.000 9.000 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit 1 9.000 12.000 24.000 2 4.000 8.000 9.000 3 2.400 3.000 No Upper Limit a. What is the optimal solution including the optimal value of the objective function? b. Suppose the profit on x1 is…