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# Optimizing Product Mix :Linear programming

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Optimizing Product Mix. California Products Company has the capability of producing and selling three products. Each product has an annual demand potential (at current pricing and promotion levels), a variable contribution, and an annual fixed cost. The fixed cost can be avoided in the product is not produced at all. This information is summarized as follows:

Product Demand Contribution Fixed Cost
I 290,000 \$1.20 \$60,000
J 200,000 \$1.80 200,000
K 50,000 \$2.30 55,000

Each product requires work on three machines. The standard productivities and capacities are as follows:

Hours per 1,000 Units

Hours
Machine Product I Product J Product L Available
A 3.205 3.846 7.692 1,900
B 2.747 4.808 6.41 1,900
C 1.923 3.205 9.615 1,900

a. Determine which products should be produced, and how much of each should be produced, in order to maximize profit contribution from these operations.
b. Suppose the demand potential for product K were doubled. What would be the maximum profit contribution?

https://brainmass.com/economics/production-function/optimizing-product-mix-linear-programming-140548

#### Solution Summary

Solution explains which products should be produced, and how much of each should be produced, in order to maximize profit contribution from these operations.and calculation of the maximum profit contribution.

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## Linear Programming : Optimizing Product Mix

The Androgynous Bicycle Company (ABC) has the hottest new products on the upscale toy market -- boys' and girls' bicycles in bright fashion colors, with oversized hubs and axles, shell design safety tires, a strong padded frame, chrome-plated chains, brackets and valves, and a non-slip handlebar. Due to the seller's market for high-quality toys, ABC can sell all the bicycles it manufactures at the following prices: boys' bikes -- \$220, girls' bikes -- \$175. This is the price payable to ABC at its Orlando plant.

The firm's accountant has determined that direct labor costs will be 45% of the price ABC receives for the boys' model and 40% of the price received for the girls' model. Production costs other than labor, but excluding painting and packaging, are \$44 per boys' bicycle and \$30 per girls' bicycle. Painting and packaging are \$20 per bike, regardless of model.

The Orlando plant's overall production capacity is 390 bicycles per day. Each boy's bike requires 2.5 labor hours while each girl's model takes 2.4 hours to complete. ABC currently employs 120 workers, who each work an 8-hour day. The firm has no desire to hire or fire employees to affect labor availability, believing its stable work force is one of its biggest assets.

a. Formulate a linear programming model that can be used to develop a product mix for the company that yields an optimal profit contribution.
b. Determine the optimal product mix using the Management Scientist software.
c. Explain the impact (if any) on the optimal solution resulting from the stable workforce policy adopted by the firm.

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