A production manager is faced with the question of how to allocate the manufacturing of a microwave oven between his own company and a subcontractor, because neither firm can handle the demand alone.

Fabrication costs are $10 per unit within the company and $20 per unit from the subcontractor; assembly costs are $8 per unit within the company and $5 from the subcontractor; and inspection costs are $3 per unit within the company and $1 per unit from the subcontractor. The company has a budget of $120,000 for fabrication, $40,000 for assembly, and $12,000 for inspection. The contribution to profits is $60 per unit regardless of which firm does the work.

Formulate this problem as a linear problem model.

Solution Preview

Let X and Y respectively be the units of microwave oven produced by the company and the subcontractor. Let C be the contribution to profit.

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