Here is a 5 by 5 assignment problem.82 36 227479 72120 28 75 109 4427 69 7 9612 41 61 24 23The problem is to meet the demand for minimal cost.Use the Hungarian algorithm to obtain the optimal solution and6971571493fill in your value for minimum cost: Here is the optimal tableau for a standard Max problem.21000X1-0100X2X3X4 81S2$3 rhs530650.37.50-.1.2028360 0-8121-1/15 -3 1 1/15 -1/10 0The following new constraint must be incorporated (i.e. Change 6):50 x1+30 x2 + 15 x3 + 20 x4 ≥ 350what is the value of the left side of this new constraint with the current optimal solution?What is the new optimal value of z?27006602ہےTo use Dual Simplex to get the new optimal solution, change this new constraint to a constraint and add a row (and an $4column).

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Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 53P

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Another way to derive a demand function is to break the market into segments and identify a low price, a medium price, and a high price. For each of these prices and market segments, we ask company experts to estimate product demand. Then we use Excels trend curve fitting capabilities to fit a quadratic function that represents that segments demand function. Finally, we add the segment demand curves to derive an aggregate demand curve. Try this procedure for pricing a candy bar. Assume the candy bar costs 0.55 to produce. The company plans to charge between 1.10 and 1.50 for this candy bar. Its marketing department estimates the demands shown in the file P07_47.xlsx (in thousands) in the three regions of the country where the candy bar will be sold. What is the profit-maximizing price, assuming that the same price will be charged in all three regions?
This problem is based on Motorolas online method for choosing suppliers. Suppose Motorola solicits bids from five suppliers for eight products. The list price for each product and the quantity of each product that Motorola needs to purchase during the next year are listed in the file P06_93.xlsx. Each supplier has submitted the percentage discount it will offer on each product. These percentages are also listed in the file. For example, supplier 1 offers a 7% discount on product 1 and a 30% discount on product 2. The following considerations also apply: There is an administrative cost of 5000 associated with setting up a suppliers account. For example, if Motorola uses three suppliers, it incurs an administrative cost of 15,000. To ensure reliability, no supplier can supply more than 80% of Motorolas demand for any product. A supplier must supply an integer amount of each product it supplies. Develop a linear integer model to help Motorola minimize the sum of its purchase and administrative costs.
Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows: 14, 58, 912, 1316, and 1720. a. Find the optimal investments when at most one investment from each group can be selected. b. Find the optimal investments when at least one investment from each group must be selected. (If the budget isnt large enough to permit this, increase the budget to a larger value.)
Given this linear programming model, solve the model and then answer the questions that follow.Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc.Subject toMachine 5x1 + 4x2 + 3x3 ≤ 160 minutes Labor 4x1 + 10x2 + 4x3 ≤ 288 hoursMaterials 2x1 + 2x2 + 4x3 ≤ 200 poundsProduct 2 x2 ≤ 16 units x1, x2, x3 ≥ 0 a. Are any constraints binding? If so, which one(s)?
You are given the tableau shown in Table 74 for amaximization problem. Give conditions on the unknowns a1, a2, a3, b, and c that make the following statements true: a The current solution is optimal. b The current solution is optimal, and there are alternativeoptimal solutions. c The LP is unbounded (in this part, assume that b0).
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The CFO for the Shelton Corporation has $1.2 million to allocate to the following budget requests from five departments: Dept. 1 Dept. 2 Dept. 3 Dept. 4 Dept. 5 $450,000 $310,000 $275,000 $187,500 $135,000 Because the total budget requests exceed the available $1.2 million, not all the requests can be satisfied. Suppose the CFO wants to make sure each department receives at least 70% of the requested amount. Further, suppose the CFO considers the requests for departments 2 and 3 to be twice as important as those from departments 4 and 5, and the request from department 1 to be twice as important as those from departments 2 and 3. The CFO want to minimize the sum of the weighted deviations from the goals. What is the optimal sum of weighted deviations? a. 0.96 b. 1.00 c. 0.00 d. 218.25
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Here is a 5 by 5 assignment problem. 69 14 82 36 22 71 93 74 79 120 28 75 109 44 27 69 7 96 12 41 61 24 23 The problem is to meet the demand for minimal cost. 57 72 Use the Hungarian algorithm to obtain the optimal solution and fill in your value for minimum cost: 0