HW#3A.sol.2010W.rev

HW#3A.sol.2010W.rev - Question 1 (45 marks) Fred Johanasson...

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Question 1 (45 marks) Fred Johanasson (a) The 3 decisions facing Fred are: How many kilograms of corn to include in the daily diet How many kilograms of tankage to include in the daily diet 3 marks How many kilograms of alfalfa to include in the daily diet (b)The costs of all three ingredients are relevant costs. 1 mark This is because the costs of all 3 ingredieints have been included in the target cel 1 mark c) See attached Model 1 13 marks (d) The total weight to feed each pig per day is 3.57 kg (1.14 + 0.00 + 2.43) 2 marks (e) $1.06 (3.48 - 2.42) 2 marks Note: This is determeined by re-running the model with C = 1, T = 2 and A = 2 (f) The 20%-to 35% corn constraint HAS NO EFFECT on the value of the target cell. 1 mark Because these constraints are NON_BINDING 1 mark (g) The optimal soluion is: Corn = 1.14 kg Tankage = 0.00 kg 3 mark Alfalfa = 2.43 kg (h) For each reduction in the carbohydrate level not required the Target Cell will go down by $0.007714286 New TOTAL COST: $2.30 (.007714286 x 15) 3 marks (i) See Model 1 attached 2 marks See Sensitivity Report1 attached 2 marks Part (j) (11 marks) Let C = # kilograms of corn in the daily diet Let T = # kilograms of Tankage in the daily diet 3 marks Let A = # kilograms of Alfalfa in the daily diet Minimize 0.84C + 0.72T + 0.60A 1 mark subject to: 90C + 20T + 40A >= 200 30C + 80T + 60A >= 180 10C + 20T + 60A >= 150 C <= 0.35(C +T+A) 7 marks C >= 0.20(C +T + A) (1 mark each) A + T >= 0.60 ( C + T + A) C,T,A >= 0 1 mark for the answer; 1 mark for showing the calculations to determine that number 1 mark for the answer; 2 marks for showing the calculation Question 1
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Question #1 Fred Jonasson Farms (Parts c and d) Input Items Nutritional Each Kilogram of Model Model Ingredient Corn Tankage Alfalfa Output Requirement Carbohydrates 90 20 40 200 200 units Proteins 30 80 60 180 180 units Vitamins 10 20 60 157 150 units Total Cost Unit Cost 0.84 $ 0.72 $ 0.60 $ $2.42 Solution Action Plan Corn Tankage Alfalfa Total Weight # of kilograms of 1.14 0.00 2.43 3.57 Additional Constraints (Blending Constraints) Model Model Output Requirement Corn 1.14 <= 1.25 kg Corn must be at most 0.35 of Total Weight Corn 1.14 >= 0.71 kg Corn must be at least 0.20 of Total Weight Tankage + Alfalfa 2.43 >= 2.14 kg Tankage + Alfalfa must be at least 0.60 of Total Weight
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HW#3A.sol.2010W.rev - Question 1 (45 marks) Fred Johanasson...

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