Introduction to Management Science, 10e (Taylor) Chapter 3 Linear Programming: Computer Solution and Sensitivity Analysis 1) The reduced cost (shadow price) for a positive decision variable is 0. 2) When the right-hand sides of 2 constraints are both increased by 1 unit, the value of the objective function will be adjusted by the sum of the constraints’ prices. 3) When a linear programming problem is solved using a computer package decision variables will always be integer and therefore decision variable values never need to be rounded. 4) Sensitivity ranges can be computed only for the right hand sides of constraints. 5) Sensitivity analysis determines how a change in a parameter affects the optimal solution. 6) The sensitivity range for an objective function coefficient is the range of values over which the current optimal solution point (product mix) will remain optimal. 7) The sensitivity range for an objective function coefficient is the range of values over which the profit does not change. 8) The sensitivity range for a constraint quantity value is the range over which the shadow price is valid. 9) If we change the constraint quantity to a value outside the sensitivity range for that constraint quantity, the shadow price will change. 10) The sensitivity range for a constraint quantity value is the range over which the optimal values of the decision variables do not change. 11) Linear programming problems are restricted to decisions in a single time period. Answer: FALSE 12) A maximization problem may be characterized by all greater than or equal to constraints. 13) A change in the value of an objective function coefficient will always change the value of the optimal solution. 14) The terms reduced cost, shadow price, and dual price all mean the same thing. 15) Sensitivity analysis can be used to determine the effect on the solution for changing several parameters at once. 16) For a profit maximization problem, if the allowable increase for a coefficient in the objective function is infinite, then profits are unbounded. 17) The reduced cost (shadow price) for a positive decision variable is __________. 18) The sensitivity range for a __________ is the range of values over which the quantity values can change without changing the shadow price 19) __________ is the analysis of the effect of parameter changes on the optimal solution. 20) The sensitivity range for a constraint quantity value is also the range over which the __________ is valid. 21) The sensitivity range for an __________ coefficient is the range of values over which the current optimal solution point (product mix) will remain optimal. Consider the following linear program, which maximizes profit for two products, regular (R), and super (S): MAX 50R + 75S s.t. 1.2R + 1.6 S ? 600 assembly (hours) 0.8R + 0.5 S ? 300 paint (hours) .16R + 0.4 S ? 100 inspection (hours) Sensitivity Report: Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$7 Regular = 291.67 0.00 50 70 20 $C$7 Super = 133.33 0.00 75 50 43.75 Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $E$3 Assembly (hr/unit) 563.33 0.00 600 1E+30 36.67 $E$4 Paint (hr/unit) 300.00 33.33 300 39.29 175 $E$5 Inspect (hr/unit) 100.00 145.83 100 12.94 40 22) The optimal number of regular products to produce is __________, and the optimal number of super products to produce is __________, for total profits of __________. 23) If the company wanted to increase the available hours for one of their constraints (assembly, painting, or inspection ) by 2 hours, they should increase __________. 24) The profit on the super product could increase by __________ without affecting the product mix. Key words: computer solution 25) If downtime reduced the available capacity for painting by 40 hours (from 300 to 260 hours), profits would be reduced by __________. 26) A change in the market has increased the profit on the super p…
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