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Chapter 03

# Chapter 03 - CHAPTER 3 LINEAR PROGRAMMING MODELING...

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CHAPTER 3 LINEAR PROGRAMMING MODELING APPLICATIONS WITH COMPUTER ANALYSES IN EXCEL SOLUTIONS TO PROBLEMS 3-1. Let F = number of French Provincial cabinets produced each day, and D = number of Danish Modern cabinets produced each day Objective: Maximize revenue = \$28F + \$25D Subject to 3F + 2D ≤ 360 hours (carpentry department) 1½F + 1D ≤ 200 hours (painting department) ¾F + ¾D ≤ 125 hours (finishing department) F ≥ 60 units (contract requirement) D ≥ 60 units (contract requirement) Solution: See file P3-1.XLS. Produce 60 French Provincial cabinets and 90 Danish Modern cabinets per day. Profit = \$3,930. 3-2. Let C = number of canvas backpacks produced. P, N, L defined similarly. Objective: Maximize profit = (Canvas revenue – Canvas cost)*C + (Plastic revenue – Plastic cost)*P + (Nylon revenue – Nylon cost)*N + (Leather revenue – Leather cost)*L = Maximize \$14.88C + \$18.80P + \$12.80N + \$27.83L Subject to: 2.25C 200 Canvas available 2.40P 350 Plastic available 2.10N 700 Nylon available 2.60L 550 Leather available 1.5C + 1.5P 90 Canvas & Plastic labor 1.7N 42. 5 Nylon labor 1.9 L 80 Leather labor C, P, N, L 40 Max production C, P, N, L 15 Min production Solution: See File P3-2N.XLS. Produce 20 Canvas, 40 Plastic, 25 Nylon, and 40 Leather backpacks. Profit = \$2,483.58. 3-3. Let I = no. of units of internal modems produced per week E = no. of units of external modems produced per week C = no. of units of circuit boards produced per week

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F = no. of units of floppy disk drives produced per week H = no. of units of hard drives produced per week M = no. of units of memory boards produced per week Objective function analysis: First find the time used on each test device: Hours on test device 1 = (7I + 3E + 12C + 6H + 18F + 17M)/60 Hours on test device 2 = (2I + 5E + 3C + 2H + 15F + 17M)/60 Hours on test device 3 = (5I + 1E + 3C + 2H + 9F + 2M)/60 Thus, the objective function is: Maximize profit = revenue - material cost - test cost = 200I + 120E + 180C + 130F + 430H + 260M - 35I - 25E - 40C - 45F - 170H - 60M – 15(7I + 3E + 12C + 6H + 18F + 17M)/60 – 12(2I + 5E + 3C + 2H + 15F + 17M)/60 – 18(5I + 1E + 3C + 2H + 9F + 2M)/60 = \$161.35I + \$92.95E + \$135.50C + \$82.50F + \$249.80H + \$191.75M Subject to (7I + 3E + 12C + 6H + 18F + 17M)/60 120 hours (2I + 5E + 3C + 2H + 15F + 17M)/60 120 hours (5I + 1E + 3C + 2H + 9F + 2M)/60 100 hours All variables 0 Solution: See file P3-3.XLS. Produce 496.55 internal modems and 1,241.38 external modems only. Profit = \$195,504.83. 3-4. Let J = number of Junior travel pillows to produce. T and D defined similarly. Objective: Maximize profit. Calculate (Revenue – Cost) for each model, and add them to obtain the total profit. This reduces to: Profit = \$1.62J + \$1.33T + \$1.33D Subject to: 0.10 J + 0.15 T + 0.20 D 450 Cutting hours available 0.05 J + 0.12 T + 0.18 D 550 Sewing hours available 0.18 J + 0.24 T + 0.20 D 600 Finishing hours available 0.20 J + 0.20 T + 0.20 D 450 Packing hours available J, T, D 1200 Maximum production J, T, D 300 Minimum production Solution: See file P3-4.XLS. Produce 1,200 Junior, 750 Travel, and 300 Deluxe pillows. Profit = \$3,340.50. 3-5. Let C = number of cheese pizzas to order. P and V defined similarly.
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Chapter 03 - CHAPTER 3 LINEAR PROGRAMMING MODELING...

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