Assignment2_S07

Assignment2_S07 - Additional Assignment #2 Problems 4.5 a)...

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Additional Assignment #2 Problems 4.5 a) The activities are the production rates of products 1, 2, and 3. The limited resources are hours available per week on the milling machine, lathe, and grinder. b) The decisions to be made are how many of each product should be produced per week. The constraints on these decisions are the number of hours available per week on the milling machine, lathe, and grinder as well as the sales potential of product 3. The overall measure of performance is total profit, which is to be maximized. c) milling machine: 9(# units of 1) + 3(# units of 2) + 5(# units of 3) ≤ 500 lathe: 5(# units of 1) + 4(# units of 2) ≤ 350 grinder: 3(# units of 1) + 2(# units of 3) ≤ 150 sales: (# units of 3) ≤ 20 Nonnegativity: (# units of 1) ≥ 0, (# units of 2) ≥ 0, (# units of 3) ≥ 0 Profit = $50(# units of 1) + $20(# units of 2) + $25(# units of 3) d) 1 2 3 4 5 6 7 8 9 10 11 12 A B C D E F G Product 1 Product 2 Product 3 Unit Profit $50 $20 $25 Hours Hours Machine Hours Used per Unit of Product Used Available Milling machine 9 3 5 500 Š 500 Lathe 5 4 0 350 Š 350 Grinder 3 0 2 118.571 Š 150 Product 1 Product 2 Product 3 Total Profit Production Rate 26.190 54.762 20 $2,904.76 (per week) Š Sales Potential 20 Data cells: B2:D2, B5:D7, G5:G7, and D12 Changing cells: B10:D10 Target cell: G10 Output cells: E5:E7 3 4 5 6 7 E Hours Used =SUMPRODUCT(B5:D5,$B$10:$D$10) =SUMPRODUCT(B6:D6,$B$10:$D$10) =SUMPRODUCT(B7:D7,$B$10:$D$10) 9 10 G Total Profit =SUMPRODUCT(B2:D2,B10:D10) 4-1
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e) Let x 1 = units of product 1 produced per week x 2 = units of product 2 produced per week x 3 = units of product 3 produced per week Maximize Profit = $50 x 1 + $20 x 2 + $25 x 3 subject to 9 x 1 3 x 2 + 5 x 3 ≤ 500 hours 5 x 1 + 4 x 2 ≤ 350 hours 3 x 1 + 2 x 3 ≤ 150 hours x 3 ≤ 20 and x 1 ≥ 0, x 2 ≥ 0, x 3 ≥ 0. 4.6
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Assignment2_S07 - Additional Assignment #2 Problems 4.5 a)...

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