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Linear Programming and the Product-Mix Decision

Chapter Eleven (partial). Linear Programming and the Product-Mix Decision. Short-Term Product Mix Decision. How to make best use out of existing resources? That is, how to choose the best short-term product mix?

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Linear Programming and the Product-Mix Decision

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  1. Chapter Eleven (partial) Linear Programming and the Product-Mix Decision

  2. Short-Term Product Mix Decision How to make best use out of existing resources? That is, how to choose the best short-term product mix? Continuing with the Windbreaker’s Inc. example assume one production constraint: The Windy and Gale jackets are manufactured in the same plant—both require an automated sewing machine for assembly. There are 3 machines that can be run up to 20 hours per day, 5 days per week (1,200 hours per month). The demand for both jackets exceeds the capacity of the 3 machines (i.e., there is one production constraint or limiting resource).

  3. Short-Term Product Mix Decision: One Production Constraint The goal is to maximize contribution margin, subject to the production resource constraint. For this, we need to determine each product’s contribution margin per unit of the scare resource:

  4. Short-term Product Mix Decision:One Production Constraint 36,000– Production constraint for sewing machine. All possible sales mixes are represented on this line. Units of Sales for Gale Units of Sales for Windy 24,000– Slope = -36,000 ÷ 24,000 = -3/2Intercept = 36,000

  5. Short-term Product-Mix Decision:One Production Constraint Production of Windy is favored over production of Gale ($192,000 - $144,000). When there is one constraint, one of the products will be favored over the others.

  6. Short-term Product-Mix Decision:Two Production Constraints In the presence of two or more production constraints, determining the best sales mix becomes more complicated, but the principle is the same. Continuing with the Windbreaker’s Inc. example: The completed jackets are inspected and labels are added before packaging. Forty workers are required for this operation. Each of the 40 workers works 35 productive hours per week...thus, 5,600 hours are available per month for inspecting and packaging.

  7. Short-term Product-Mix Decision:Two Production Constraints For this constraint, the results are as follows:

  8. Short-term Product-Mix Decision:Two Production Constraints 67,200– Production constraint for Inspection and Packaging Maximum contribution margin 20,800 units of Windy and 4,800 units of Gale 36,000– Units of Sales for Gale Production constraint for sewing machine Units of Sales for Windy 22,400– 24,000– Corner Point Analysis

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