2017 Practice LP Problems 7 – 10 Sensitivity Analysis Answers.docx

2017 Practice LP Problems 7 – 10 Sensitivity Analysis Answers.docx

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Practice LP Problems 7 – 10 – Sensitivity Analysis Answers 7. The sensitivity report generated by Solver is provided below. a) A recent analysis of sales from the real estate guide has revealed that demand has fallen. Consequently, several advertisers have indicated that they will either pull or reduce the size of their ads in the real estate guide. Management has estimated that the impact of losing these advertisements could reduce revenues for the real estate guide to $0.65 per magazine. What impact will this have on the solution and the company’s net advertising profits? A reduction in real estate guide revenues from $.75 to $.65 will reduce the profit margin from $0.5 to $0.4. Since this is a change in a coefficient in the objective function, this is a Range of Optimality question. The Range for the coefficient is .33 .5 ∞. A new profit margin of $0.4 falls inside the R of O, therefore the solution will stay the same. The value of Z will change because a coefficient changed. The new value of Z will = $7640 – (10,000 * .1) = $7640 - $1000 = $6640.
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b) If Island Publishing Company could increase either its publication budget or the rack space for displaying its magazines, which would it choose to do and why? The budget constraint is a non-binding constraint with an upper limit of ∞. (The range of feasibility is 3860 RHS ∞.) The rule says that any change to the RHS of a non- binding constraint that is inside of its range of feasibility will have no impact on the solution or the value of Z. Therefore, increasing the budget (the RHS) by any amount will fall inside this range and will have no impact on either the solution or the total new advertising profits. Rack space, however, is a binding constraint, meaning the company is using every bit of space available. Because the constraint is binding, changing the RHS WILL change the solution. If the solution changes, the value of Z will change. The range of feasibility for rack space is 16000 RHS 18560. Every additional guide that can be displayed, up to additional space for 560 guides, will increase total net advertising profits by $0.50. Therefore, it would be beneficial for the company to get 560 more spaces to display guides. We can use the shadow price of $0.50 because we are talking about changing the RHS by a quantity that falls in the range of feasibility). We cannot tell what the new solution will be from the current printout. But, because the 560 change in the RHS is still in the range (at the upper end), we can use the Shadow Price to determine the new total net advertising profits. The value of Z will increase by (560 * $0,50 = $280). The new total net profits will be $7920 c) The Whole Foods Market has agreed to add a display rack for Island Publishing Company’s two publications. As a result of these additional display racks, Island Publishing Company’s total display space will increase by 1500 copies. What impact will this have on the solution and the company’s net advertising profits?
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