Linear Programming -- Objective Sensitivity

# How much would the cost have to be reduced profit be

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How much would the cost have to be reduced (profit be increased) so that it would be profitable to make X 1 ’s? Question 2 If X 1 were at least 1, how would the profit be affected?

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Answer to Question 1 Answer to Question 1 When slope of objective function line equals slope of time constraint line, optimal solutions exist with X 1 >0: Objective function: Objective function: C C 1 X 1 + 5X 2 Time Constraint: 3X 1 + 4X 2 ≤ 2400 Thus, C1 C1 /5 = 3/4 or C1 C1 = 3.75 Per unit profit of product 1 has to be increased to \$3.75 to make production of 1 profitable; profit has to be increased Increased Profit = 3.75 – 1 = 2.75 Increased Profit = 3.75 – 1 = 2.75 Reduced Cost Reduced Cost = 1 – 3.75 = -2.75 -2.75
Answer to Question 2 Answer to Question 2 If X 1 ≥ 1, how is the profit affected? Max. 1 1 X 1 + 5X 2 ST 2X 1 + 1X 2 ≤ 1000 (Plastic) 3X 1 + 4X 2 ≤ 2400 (Time) 1X 1 + 1X 2 700 (Limit) 1X 1 - 1X 2 350 (Product mix) X 1 1 (Requirement of X 1 ) Solution is X 1 = 1, 1, X 2 = 599.25, 599.25, New Optimal Profit = 2997.25 Reduced Cost Reduced Cost = 2997.25 – 3000 = -2.75 -2.75

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Reduced Cost on Excel Reduced Cost on Excel Here is the printout out of the sensitivity analysis dealing with the objective function coefficients for the problem. Reduced Costs
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How much would the cost have to be reduced profit be...

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