Linear Programming -- Objective Sensitivity

# The amount by which the coefficient can decrease or

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The amount by which the coefficient can decrease or increase is what Excel called the ALLOWABLE DECREASE ALLOWABLE DECREASE and the ALLOWABLE ALLOWABLE INCREASE INCREASE of the objective function coefficient. The range of values of this coefficient from the (Original Coefficient – Allowable Decrease) to (Original Coefficient + Allowable Increase) is called the Range of Optimality Range of Optimality for the coefficient.

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Range of Optimality On Excel Range of Optimality On Excel Here is the printout out of the sensitivity analysis dealing with the objective function coefficients for the original Galaxy Industries problem. Range of Optimality for C 1 8 – 4.25  8 + 2 3.75  10 Range of Optimality for C 2 5 – 1  5 + 5.666667 4  10.666667 Range of Optimality Range of Optimality is the range of values that an objective function coefficient can assume without changing the optimal solution as long as no other changes are made .
Reduced Cost Reduced Cost 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 , X 2 ≥ 0 The optimal solution is X X 1 1 = 0, X = 0, X 2 = 600, = 600, objective function = 3,000 = 3,000 No product 1 were produced because its unit profit was not large enough.

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Questions Questions Question 1 How much would the cost have to be reduced (profit be increased) so that it would be profitable to make X 1 ’s?
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