Chirality Company must produce at least 600,000 small screws and 400,000 large s
ID: 390616 • Letter: C
Question
Chirality Company must produce at least 600,000 small screws and 400,000 large screws to meet the demands for the next 4 weeks. These screws can be produced on two different machines, which are each available for 60 hours per week. The costs and time requirements for producing each size screw on each machine and the selling price of each size screw are given in the following table:
Small Screws
Large Screws
Selling price ($/1000)
Cost on Machine 1 ($/1000)
Cost on Machine 2 ($/1000)
Time on Machine 1 (min/lb)
Time on Machine 2 (min/lb)
There are about 60 small screws in each pound and 40 large screws in each pound. Using the variables
The Production Manager has formulated the following model to maximize the profit and meet the demand with the limited availability of machine time in the next four weeks:
Maximize 27.50S1 + 27.50S2 + 32.50L1 + 32.50L2
Subject to
S1 + S2 600,000
L1 + L2 400,000
1.5S1 + 1.75L1 60
1.0S1 + 1.25L2 60
S1, S2, L1, L2 0
Is this model correct? If not, identify and correct all mistakes.
Small Screws
Large Screws
Selling price ($/1000)
27.50 32.50Cost on Machine 1 ($/1000)
6.25 7.75Cost on Machine 2 ($/1000)
8.00 9.25Time on Machine 1 (min/lb)
1.50 1.75Time on Machine 2 (min/lb)
1.00 1.25Explanation / Answer
Profit per small screw produced on machine 1 (S1)= (27.5-6.25)/1000 = 21.25/1000 = 0.02125
Profit per large screw produced on machine 1 (L1) = (32.50-7.75)/1000 = 0.02475
Profit per small screw produced on machine2 (S2) -0.0195
Profir per large screw on machine 2 (L2) - 0.02325
Objective function
Max (0.02125 S1+ 0.02475L1 + 0.0195S2+0.02325L2)
subject to
S1+S2 =>600000
L1+L2=>400000
1.50/60 S1 +1.75/40 L1 <=3600
1/60S2+1.25/40L2 <= 3600
S1, S2, L1,L2 =>0
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