solution

A company has recently received an order including various quantities of three “models” of a product. The order quantities and resource requirements of these models are summarized in the following table.

	Model 1	Model 2	Model 3
Number ordered	3,000	2,000	900
Hours of assembly required per unit	2	1.5	3
Hours of finishing required per unit	1	2	1

Although the company has only 10,000 hours of assembly capacity and 5,000 hours of finishing capacity, it can outsource any portion of the order to a subcontractor. The following table includes the cost of making and the cost of buying per unit for each model.

	Model 1	Model 2	Model 3
Cost to Make	$50	$83	$130
Cost to Buy	$61	$97	$145

Formulate an algebraic model to determine the make and buy quantities for each model minimizing the cost of fulfilling the customer order.