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Consider the following linear program, which maximizes profit for two products--regular (R) and super (S): Maximize: 100R + 150S t. .OR + 2.5 Ss 250 Wiring (hours) .OR + 2.5 Ss 320 Welding (hours) .OR + 4.0 Ss300 Inspection (hours)

Consider the following linear program, which maximizes profit for two products--regular (R) and super (S): Maximize: 100R + 150S t. .OR + 2.5 Ss 250 Wiring (hours) .OR + 2.5 Ss 320 Welding (hours) .OR + 4.0 Ss300 Inspection (hours)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following linear program, which maximizes profit for two products--regular (R) and super (S): Maximize: 100R + 1505 s.t. 1.0 R + 2.5 5< 250 Wiring (hours) 4.0 R + 2.5 S s 320 Welding (hours) 1.0 R + 4.0 Ss 300 Inspection (hours) Sensitivity Report: Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $857 Regular = 39.26 0.00 100 140 62.5 $C$7 Super = 65.19 0.00 150 250 87.5 Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease SES3 Wiring (hr/unit) SES4 Welding (hr/unit) 202.22 250 1E+30 47.78 320 18.52 320 430 132.5 SESS Inspection (hr/unit) 300 25.93 300 86 220 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 and the optimal number of super products to produce is , for total profits of S i) If the company wanted to increase the available hours for one of their constraints by two hours, they should increase iim) The profit on the super product could increase by $ without affecting the product mix. iv) If downtime reduced the available capacity for wiring by 40 hours, the profit would be reduced by $ v) A change in the market has increased the profit on the super product by $5. Total profit will increase by $ vi) If the company wanted to decrease the available hours for one of their constraints by eight hours, they should decrease vii) The number of slack hours in wiring is vii) Shadow price of inspection can be increased from $25.93 to $86 without affecting the product mix (
Transcribed Image Text:Consider the following linear program, which maximizes profit for two products--regular (R) and super (S): Maximize: 100R + 1505 s.t. 1.0 R + 2.5 5< 250 Wiring (hours) 4.0 R + 2.5 S s 320 Welding (hours) 1.0 R + 4.0 Ss 300 Inspection (hours) Sensitivity Report: Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $857 Regular = 39.26 0.00 100 140 62.5 $C$7 Super = 65.19 0.00 150 250 87.5 Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease SES3 Wiring (hr/unit) SES4 Welding (hr/unit) 202.22 250 1E+30 47.78 320 18.52 320 430 132.5 SESS Inspection (hr/unit) 300 25.93 300 86 220 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 and the optimal number of super products to produce is , for total profits of S i) If the company wanted to increase the available hours for one of their constraints by two hours, they should increase iim) The profit on the super product could increase by $ without affecting the product mix. iv) If downtime reduced the available capacity for wiring by 40 hours, the profit would be reduced by $ v) A change in the market has increased the profit on the super product by $5. Total profit will increase by $ vi) If the company wanted to decrease the available hours for one of their constraints by eight hours, they should decrease vii) The number of slack hours in wiring is vii) Shadow price of inspection can be increased from $25.93 to $86 without affecting the product mix (
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