1. (30 pts.) A company that manufactures three products, A, B, and C, using three machines, M1, M2, and M3, wants to determine the optimal production schedule that maximizes the total profit. Product has to be processed by machines M1, M2, and M3, product B requires M1 and M3, while product Crequires M1 and M2. The unit profits on the three products are $4, $2, and $5, respectively. The following linear program is formulated to determine the optimal product mix: Maximize Z=4x+2x2+5x3 5.L x+2x2+ x ≤430 (Machine 1) 3x + 2x ≤ 460 (Machine 2) x+4x2 ≤450 (Machine 3) and 11.12.20 where x1, x2, and xs are the amounts of products A. B, and C and the constraints reflect the available capacities of M1, M2, and M3. The optimum solution for the problem is as follows: optimal solution: -0, -100, x-230 optimal value: maximum profit, Z=1350 shadow prices: 1.0, 2.0, and 0.0 for constraints 1, 2 and 3 respectively reduced costs: for x 3.0, for x = 0, for x)=0 RANGES ON RIGHT-HAND-SIDE (RHS) CONSTRAINTS Row Lower Limit Present Value Upper Limit 1 230 430 455 2 410 460 860 3 400 450 8 RANGES ON OBJECTIVE FUNCTION COEFFICIENTS Variable Lower Limit Present Value Upper Limit F 88 4.0 7.0 32 0 2.0 10.0 F 3.0 5.0 8 Using the above information answer the following questions: a. Because of an increase in the cost of raw material used for product C, its unit profit drops to $4. Determine the new optimal solution and the maximum profit. b. Suppose it is possible to increase the capacity of one of the machines. Which one would you recommend for expansion and why? C Due to an improvement in product design, the unit profit on product A can be increased to $6. Is it worthwhile producing product.A now? Explain. d. Suppose that the capacity of machine 2 can be increased by another 200 minutes at a cost of $250. Is it economical to do so? Explain. c. Because of an increase in the cost of energy for operating the machines, the unit profits of 4, B, and C decrease by $2.0, $0.5, and $1.0, respectively. How will it affect the optimal solution and maximum profit?

Leary and O’Donnell, a local CPA firm, has been asked to bid on a contract to perform audits for three counties in its home state. Because existing staff are fully scheduled, if the firm is awarded the contract, it must hire one new staff member at a salary of $63,000 to handle the additional workload. The managing partner is convinced that obtaining the contract will lead to additional new clients from the respective counties. Expected new work (excluding the three counties) is 860 hours at an average billing rate of $90 per hour. Other information follows about the firm’s current annual revenues and costs:   Firm volume in hours (normal) 30,750   Fixed costs $ 575,000   Variable cost $ 35 /hour   Should the firm win the contract, the audits of the three counties will require 840 hours of expected work.   Required: 1. If the managing partner’s expectations are correct, what is the lowest bid the firm can submit and still expect to increase annual net income? What would be…

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M8

1. A major supermarket chain has decided to sub-contract production of ready-to-eat sandwiches to your production plant. Your plant can make three kinds of sand- wiches, each of which take the following amounts of raw ingredients (measured in grams) to produce: Sandwich | Chicken Cheese Lettuce Tomato Bread 45 15 25 10 13 Chicken Salad Chicken Club Cheese and salad 920 0 20 30 Chicken Salad Chicken Club Cheese and Salad 15 10 20 The total amount of time (measured in minutes) to make one of each sandwich is listed below, together with the price that the supermarket will pay to purchase one of each: Sandwich | Time to Make Price 2.8 4.8 1.3 60 90 60 £1.25 £1.65 £0.95 For the sake of this problem you can treat ingredients used and number of sandwiches made as continuous quantities we could perhaps think of this as the average made per day over a longer period, in which case making 100.43 sandwiches per day would still make sense. (a) Suppose that you have 5000g of chicken, 2500g of…

33 White & Becker Tools (W&B) requires 2,000 elec- tric motors next month for its product line of weed trimmers. Each motor is composed of three com- ponents: a coil, a shaft, and housing. W&B has the capability to produce these components or purchase them from an outside vendor. The costs of produc- ing them and purchasing them are shown in the following table. COMPONENT Coil Shaft Housing DEPART- MENT PRODUCTION COST PER UNIT Fabrication 0.5 Molding 0.4 Inspection 0.2 $2.60 $1.80 $1.40 The components that are produced by W&B must pass through three departments: fabrication, molding, and inspection. The number of hours each component requires in each department and the total number of hours available next month in each department are shown in the following table: 0.2 0.7 0.3 PURCHASE COST PER UNIT COIL SHAFT HOUSING AVAILABILITY (HR.) (HR.) (HR.) (HR.) $3.12 $2.16 $1.68 0.6 0.3 0.4 3,000 3,000 1,800 In order to determine the number of components that will be produced and the number…

PA 5-12 (Static) A pharmaceutical company creates... A pharmaceutical company creates a compound with a four-stage process: Heat Acid 250 kg/hr Reaction 200 kg/hr Separation 200 kg/hr 15% 45% Some of the resources have partial yields: 15 percent of material is discarded after the Acid step and 45 percent of the material is discarded after the separation step. The capacities of the last three steps are indicated in the diagram above. Instruction: Round yield of this process answer to 4 decimal places and minimum capacity answer to 2 decimal places. (a) What is the yield of this process? (b) What is the minimum capacity (kg/hr) of the first step, Heat, so that the process can yield 100kg/hr of final product?

4. Consider the following argument: If the white flag is flying, then truce has been declared. Truce has not been declared. Therefore, the white flag is not flying. (a) Define statement variables for each component of the above argument, then write the formal argument using your variables.

D3)

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