8 x 14 62 x 15 600 const 4 58 x 1 103 x2 11x3 81 x 5

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5.8 x 14 6.2 x 15 600 const 4: 5.8 x 1 10.3 x 2 1.1 x 3 8.1 x 5 7.1 x 6 6.2 x 7 7.3 x 8 10 x 9 11 x 10 12.5 x 11 13.1 x 12 15 x 15 2500 const 5: 10.9 x 1 2 x 2 2.3 x 3 4.9 x 5 10 x 6 11.1 x 7 12.4 x 8 5.2 x 9 6.1 x 10 7.7 x 11 5 x 12 2.1 x 13 1 x 15 1800 const 6: 3.1 x 1 1 x 2 1.2 x 3 4.8 x 4 5.5 x 5 0.8 x 6 9.1 x 7 4.8 x 8 1.9 x 9 1.4 x 10 1 x 11 5.1 x 12 3.1 x 13 7.7 x 14 6.6 x 15 1000 const 7: 1 x 1 0 const 8: 1 x 2 20 const 9: 1 x 3 10 const 10: 1 x 4 10 const 11: 1 x 5 0 const 12: 1 x 6 20 const 13: 1 x 7 10 const 14: 1 x 8 20 (c) Description Variables and Coefficients? What Type? RHS? C1: Cust A’s demand formula: VA1 VA2 VA3 = 650 C2: Cust B’s demand formula: VB1 VB2 VB3 = 800 C3: W1’s supply formula: VA1 VB1 < 400
449 BUSINESS ANALYTICS MODULE B L INEAR P ROGRAMMING const 15: 1 x 9 50 const 16: 1 x 10 20 const 17: 1 x 11 20 const 18: 1 x 12 10 const 19: 1 x 13 20 const 20: 1 x 14 10 const 21: 1 x 15 10 Solution Value 9683.229 Optimal Reduced Original Lower Upper Value Cost Coefficien t Limit Limit x 1 0.00 1.3237 3 18.79 Infinity 20.11373 x 2 20.00 0.00 6.31 Infinity 52.49662 x 3 10.00 0.00 8.19 Infinity 34.64475 x 4 10.00 0.00 45.88 Infinity 48.41532 x 5 11.507 0.00 63.00 59.01673 77.38298 x 6 20.00 0.00 4.10 Infinity 31.47013 x 7 10.00 0.00 81.15 Infinity 115.1911 x 8 20.00 0.00 50.06 Infinity 82.73582 x 9 50.00 0.00 12.79 Infinity 24.539 x 10 20.00 0.00 15.88 Infinity 26.7216 x 11 20.00 0.00 17.91 Infinity 27.28386 x 12 54.945 0.00 49.99 47.34072 56.43208 x 13 20.00 0.00 24.00 Infinity 53.243 x 14 12.202 0.00 88.88 80.82936 126.4764 x 15 10.00 0.00 77.01 Infinity 125.8801 The optimal solution provides a profit of $9683. Note that only product A158 is not produced. (b) The shadow prices are given in the table above. (c) There is no value to adding more workers because those available are not yet fully occupied. Solution Value = 9683.229 Shadow Slack or Original Lower Upper Prices Surplus RHS Limit Limit const 1 2.711812 0.00 980.00 861.5504 1,024.236 const 2 0.00 113.866 400.00 286.1337 Infinity const 3 10.6486 0.00 600.00 587.7851 608.5712 const 4 2.182708 0.00 2,500.00 1,889.72 2,534.683 const 5 0.00 258.885 1,800.00 1,541.115 Infinity const 6 0.00 8.52954 1,000.00 991.4705 Infinity const 7 0.00 0.00 0.00 Infinity 0.00 const 8 46.1866 0.00 20.00 17.91737 41.84552 const 9 26.4548 0.00 10.00 5.041353 19.9601 const 10 2.53532 0.00 10.00 0.00 16.993 const 11 0.00 11.5072 0.00 Infinity 11.50722 const 12 27.37 0.00 20.00 16.50255 37.096 const 13 34.041 10.00 10.00 3.532913 12.01538 const 14 32.6758 0.00 20.00 17.09391 23.00434 const 15 11.75 0.00 50.00 39.20661 116.4478 const 16 10.8416 0.00 20.00 14.30611 79.923 const 17 9.37385 0.00 20.00 15.88757 68.822 const 18 0.00 44.95 10.00 Infinity 54.94591 const 19 29.243 0.00 20.00 15.45261 22.44298 const 20 0.00 2.20215 10.00 Infinity 12.20215 const 21 48.87 0.00 10.00 8.355577 12.84913
BUSINESS ANALYTICS MODULE B L INEAR P ROGRAMMING 450 (d) Two tons of steel at a total cost of $8,000 implies a cost per pound of $2.00. Forty-four pounds of it should be purchased because the shadow price is $2.71 and the upper limit is 1,024 pounds. (e) Change coefficient for variable x 14 in objective function from 88.88 to 8.88. The following results: Solution Value = 8865.5 Optimal Reduced Original Lower Upper Value Cost Coefficie nt Limit Limit x 1 0.00 1.2391 1 18.79 Infinity 20.02911 x 2 20.00 0.00 6.31 Infinity 51.68507 x 3 10.00 0.00 8.19 Infinity 32.86478 x 4 16.993 0.00 45.88 38.60427 60.25521 x 5 7.056 0.00 63.00 42.61333 71.26741 x 6 20.00 0.00 4.10 Infinity 30.43315 x 7 10.00 0.00 81.15 Infinity 106.3944 x 8 20.00 0.00 50.06 Infinity 76.83481 x 9 50.00 0.00 12.79 Infinity 26.18145 x 10 20.00 0.00 15.88 Infinity 28.52473 x 11 20.00 0.00 17.91 Infinity 29.29111 x 12 57.697 0.00 49.99 47.574 91.778 x 13 20.00 0.00 24.00 Infinity 45.986 x 14 10.00 0.00 8.88 Infinity 80.82936 x 15 10.00 0.00 77.01 Infinity 119.6576 Solution Value = 8865.5 Shadow Slack or Original Lower Upper Prices Surplus RHS Limit Limit const 1 2.74856 0.00 980.00 913.6641 993.1374 const 2 0.00 113.879 400.00 286.1211 Infinity const 3 9.197201 0.00 600.00 587.7851 601.577 const 4 2.343288 0.00 2,500.00 2,342.00 2,512.443 const 5 0.00 266.934 1,800.00 1,533.066 Infinity const 6 0.00 2.36523 1,000.00 997.6348 Infinity const 7 0.00 0.00 0.00 Infinity 0.00 const 8 45.3751 0.00 20.00 19.45971 41.84552 const 9 24.6748 0.00 10.00 8.988791 19.9601 const 10 0.00 6.993 10.00 Infinity 16.993 const 11 0.00 7.05643 0.00 Infinity 7.056433 const 12 26.3331 0.00 20.00 19.15507 37.096 const 13 25.2444 0.00 10.00 9.459686 12.01538 const 14 26.7748 0.00 20.00 19.5257 23.00434

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