A manufacturer makes two types of tractors, the X-Harvester and the Y-Combine. The time for assembling is 3 hours for the X and 4 hours for the Y. The total assembly time allotted is 8,400 hours. Finishing the machines takes 3 hours for the X, 2.5 hours for Y. Total finishing time allotted is 5,700 hours. Packing takes 0.8 hour for X, 0.4 hour for Y. Total packing time is 1,340 hours. Profit (P) is $30,000 for each X-Harvester and $37,500 for each Y-Combine. (Use the variables X and Y, capitalized.) a) Give the objective function. Profit= b) List all 5 constraints. SAR c) List the corners of the constraint graph. (A manufacturer can produce a fraction of a machine in this period, to be finished and sold in the next period.)

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A manufacturer makes two types of tractors, the X-Harvester and the Y-Combine. The time for assembling is 3 hours for the X and 4 hours for the Y. The total assembly time
allotted is 8,400 hours. Finishing the machines takes 3 hours for the X, 2.5 hours for Y. Total finishing time allotted is 5,700 hours. Packing takes 0.8 hour for X, 0.4 hour for
Y. Total packing time is 1,340 hours. Profit (P) is $30,000 for each X-Harvester and $37,500 for each Y-Combine. (Use the variables X and Y, capitalized.)
a) Give the objective function.
Profit=
b) List all 5 constraints.
c) List the corners of the constraint graph. (A manufacturer can produce a fraction of a machine in this period, to be finished and sold in the next period.)
d) Evaluate the objective function at the corners.
i) What is the maximum profit?
ii) How many of each type of tractor should this manufacturer produce?
X-Harvesters
Y-Combines
Transcribed Image Text:A manufacturer makes two types of tractors, the X-Harvester and the Y-Combine. The time for assembling is 3 hours for the X and 4 hours for the Y. The total assembly time allotted is 8,400 hours. Finishing the machines takes 3 hours for the X, 2.5 hours for Y. Total finishing time allotted is 5,700 hours. Packing takes 0.8 hour for X, 0.4 hour for Y. Total packing time is 1,340 hours. Profit (P) is $30,000 for each X-Harvester and $37,500 for each Y-Combine. (Use the variables X and Y, capitalized.) a) Give the objective function. Profit= b) List all 5 constraints. c) List the corners of the constraint graph. (A manufacturer can produce a fraction of a machine in this period, to be finished and sold in the next period.) d) Evaluate the objective function at the corners. i) What is the maximum profit? ii) How many of each type of tractor should this manufacturer produce? X-Harvesters Y-Combines
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