Question: Consider the following linear program, which maximizes profit for two products--regular (R) and super (S): Maximize: 40R + 60S s.t. 2.0 R + 2.5 S
Consider the following linear program, which maximizes profit for two products--regular (R) and super (S):
Maximize: 40R + 60S s.t. 2.0 R + 2.5 S 140 Wiring (hours) 1.2 R + 2.5 S 200 Welding (hours) 2.0 R + 5.0 S 150 Inspection (hours) Sensitivity Report:
| Final | Reduced | Objective | Allowable | Allowable | ||
| Cell | Name | Value | Cost | Coefficient | Increase | Decrease |
| $B$7 | Regular = | 65 | 0.00 | 40 | 8 | 16 |
| $C$7 | Super = | 4 | 0.00 | 60 | 40 | 10 |
| Final | Shadow | Constraint | Allowable | Allowable | ||
| Cell | Name | Value | Price | R.H. Side | Increase | Decrease |
| $E$3 | Wiring (hr/unit) | 140 | 16 | 140 | 10 | 65 |
| $E$4 | Welding (hr/unit) | 88 | 0 | 200 | 1E+30 | 112 |
| $E$5 | Inspection (hr/unit) | 150 | 4 | 150 | 130 | 10 |
Answer the following questions from the sensitivity output of Excel Solver of an LP problem shown above:
i) The optimal number of regular products to produce is Answer24654048, and the optimal number of super products to produce is Answer10060450, for total profits of $Answer.
ii) If the company wanted to increase the available hours for one of their constraints by two hours, they should increase AnswerInspectionWeldingWiring
iii) The profit on the super product could increase by $Answer without affecting the product mix.
iv) If downtime reduced the available capacity for welding by 40 hours, the profit would be reduced by $Answer.
v) A change in the market has increased the profit on the super product by $5. Total profit will increase by Answer.
vi) If the company wanted to decrease the available hours for one of their constraints by eight hours, they should decrease AnswerWiringWeldingInspection.
vii) If downtime reduced the available capacity for Inspection by 20 hours, the profit would be reduced by $Answer.
viii) Shadow price of wiring can be increased from $16 to $26 without affecting the product m
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