Chapter 13-1 Demonstration Problem Solutions Page 1 Please send comments and corrections to me at [email protected] Demo 13-1-1 ANSWER In this problem, let I represent the number of engines shipped to plant I and II represent the number of engines shipped to plant II. The Objective Function here is to Minimize shipping costs: Min 20(I) + 35(II) The constraints here are: You can't ship more than 85 engines: I + II ≤ 85 You have to ship at least 50 engines to plant I I ≥ 50 You have to ship at least 27 engines to plant II II ≥ 27 You can't ship a negative number of engines I , II ≥ 0 Next, you graph the each of these constraints: Now, you test each corner solution: Points Objective Function: (20 I + 35 II) (50,27) 20 (50) + 35 (27) = 1000 + 945 = 1945 (50,35) 20 (50) + 35 (35) = 1000 +1225 = 2225 (58,27) 20 (58) + 35 (27) = 1160 + 945 = 2105 The minimum cost is $1945.Chapter 13-1 Demonstration Problem Solutions Page 2 Please send comments and corrections to me at [email protected] Demo 13-1-2 ANSWER In this problem, let A represent the number of units of Policy A purchased and B represent the number of units of Policy B purchased. The Objective Function here is to Minimize insurance costs: Min 50(A) + 40(B) The constraints here are: You want at least $100 coverage for fire/theft 10A + 15B ≥100 You want at least $1000 coverage for liability 80A +120B ≥1000 You can't purchase a negative number of units of insurance A , B ≥ 0 Next, you graph the each of these constraints: Now, you test each corner solution: Points Objective Function: (50 A + 40 B) (25/2,0) 50 (25/2) + 40 (0) = 625 + 0 = 625 (0,25/3) 50 (0) + 40 (25/3) = 0 + 333 = 333 The minimum cost is $333.Chapter 13-1 Demonstration Problem Solutions Page 3 Please send comments and corrections to me at [email protected] Demo 13-1-3 ANSWER ` In this problem, let A represent the number of gallons of milk purchased from Dairy A and B represent the number of gallons of milk purchased from Dairy B. The Objective Function here is to Maximize butterfat: Max .037(A) + .032(B) The constraints here are: a You can only get 50 gallons from Dairy A A ≤ 50 b You can only get 80 gallons from Dairy B B ≤ 80 c You can't buy more than 100 gallons of milk A + B ≤ 100 d You can't buy a negative number of gallons A , B ≥ 0 Next, you graph the each of these constraints: Now, you test each corner solution: Points Objective Function: (.037A + .032B) (0,80) .037 (0) + .032 (80) = 0 + 2.56 = 2.56 (20,80) .037(20) + .032 (80) = .74 + 2.56 = 3.3 (50,50) .037(50) + .032 (50) = 1.85 + 1.6 = 3.45 (50,0) .037(50) + .032 (0) = 1.85 + 0 = 1.85 The maximum butterfat is 3.45
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