Hobo manufacturing produces motorcycle parts for the manufacturer. It operates t
ID: 1198474 • Letter: H
Question
Hobo manufacturing produces motorcycle parts for the manufacturer. It operates two plants which have the following production functions: Qa=40Sa - .25Sa2 and Qb=50Sb=.5 Sb2 Where Qa is the unit output from plant A and Qb is the output from plant B. Sa and Sb are the untis of variable factor steel used at the plants. Suppose the steel availabitlity is 30 units. What is the optimal allocation between the two plants? If the availability of steel is reduced by 10 units = how should Hobo reallocate steel between the two plants? Explain????
Explanation / Answer
The allocation should give out the maximum total output.
SA SB Qa Qb Total Output 0 30 0 1050 1050 1 29 39.75 1029.5 1069.25 2 28 79 1008 1087 3 27 117.75 985.5 1103.25 4 26 156 962 1118 5 25 193.75 937.5 1131.25 6 24 231 912 1143 7 23 267.75 885.5 1153.25 8 22 304 858 1162 9 21 339.75 829.5 1169.25 10 20 375 800 1175 11 19 409.75 769.5 1179.25 12 18 444 738 1182 13 17 477.75 705.5 1183.25 14 16 511 672 1183 15 15 543.75 637.5 1181.25 16 14 576 602 1178 17 13 607.75 565.5 1173.25 18 12 639 528 1167 19 11 669.75 489.5 1159.25 20 10 700 450 1150 21 9 729.75 409.5 1139.25 22 8 759 368 1127 23 7 787.75 325.5 1113.25 24 6 816 282 1098 25 5 843.75 237.5 1081.25 26 4 871 192 1063 27 3 897.75 145.5 1043.25 28 2 924 98 1022 29 1 949.75 49.5 999.25 30 0 975 0 975 SA SB Qa Qb Total Output 0 20 0 800 800 1 19 39.75 769.5 809.25 2 18 79 738 817 3 17 117.75 705.5 823.25 4 16 156 672 828 5 15 193.75 637.5 831.25 6 14 231 602 833 7 13 267.75 565.5 833.25 8 12 304 528 832 9 11 339.75 489.5 829.25 10 10 375 450 825 11 9 409.75 409.5 819.25 12 8 444 368 812 13 7 477.75 325.5 803.25 14 6 511 282 793 15 5 543.75 237.5 781.25 16 4 576 192 768 17 3 607.75 145.5 753.25 18 2 639 98 737 19 1 669.75 49.5 719.25 20 0 700 0 700Related Questions
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