Figure 13.31 shows the sensitivity report after solving the Crebo Manufacturing
ID: 433738 • Letter: F
Question
Figure 13.31 shows the sensitivity report after solving the Crebo Manufacturing model (Example 13.12L) using Solver. Using only the information in the sensitivity report, answer the following questions. a. Explain the value of the reduced cost (0.3) for the number of plugs to produce. b. If the gross margin for rails is decreased to $1.05, can you predict what the optimal solution and profit will be? c. Suppose that the gross margin for rivets is increased to $0.85. Can you predict what the optimal solution d. If the gross margin for clips is reduced to $1.10, can you predict what the optimal solution and profit will be? e. Suppose that an additional 500 minutes of machine capacity is available. How will the optimal solution and and profit will be? What if the gross margin is reduced to $1.00?Explanation / Answer
(a)
It means that the gross margin of X1 has to increase by $0.3 before it has a basic feasible solution (i.e. solution > 0) in the optimality condition.
(b)
The allowable decrease for the coefficient of X2 is 1E+30 i.e. infinity. So, no change will be observed in the optimal solution. Also, since X2 is not is basic feasible set, the profit will also not change.
(c)
Increased to 0.85 means an increase of 0.85 - 0.75 = 0.10 which is again within the allowable increase for the coefficient of X2 i.e. 0.15. So, the optimal solution will not change. Also, since X3 is not is basic feasible set, the profit will also not change.
(d)
The reduction is 1.2 - 1.1 = 0.10 which is less than the allowable decrease which is 0.16. So, the optimal solution will not change.
However, the reduction in profit will be 140000 x 0.10 = 14000. So, the modified profit will be 168000 - 14000 = 154000
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For the reduction to $1.00, the reduction amount is $1.20 - $1.00 = $0.20 which is more than 0.16 (allowable decrease). So, the optimal solution will change although we cannot predict the change.
(e)
For the machine constraint, the allowable increase of RHS is 1E+30 i.e. infinity. So, for any increase of RHS, the shadow price of 0.60 will be intact.
So, for an increase of 500 minutes, the profit will increase by 500 x 0.60 = $300. So, the modified profit will be $168,300.
Similarly, for 300 minutes decrease, the reduction is profit will be 300 x 0.60 = $180.
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