Like many businesses, the Electrotate Company must decide whether to make their products in-house or buy them from other suppliers. Electrotate manufactures three types of slip rings (A, B, and C), which are electrical coupling devices that allow current to pass through a rotating connection. Each type of slip ring requires a certain amount of time to wire and to harness, as shown in the following table.

	Type A	Type B	Type C
Number of slip rings ordered	3,000	2,000	1,000
Wiring required per slip ring (hours)	2	1.5	3
Harnessing required per slip ring (hours)	1	2	1

Electrotate recently received a large order for their slip rings. The company only has 9,000 hours of wiring capacity and 5,000 hours of harnessing capacity to devote to this order not enough to completely make the order in-house by its due date. However, Electrotate can buy any portion of this order from one of its competitors. The unit costs of producing each type in-house and buying the finished version from a competitor are given below.

	Type A	Type B	Type C
Cost to make a unit	$50	$85	$130
Cost to buy a unit	$57	$99	$149

1) On Sheet 1: Formulate Electrotates problem as a linear program that determines the best number of slip rings to make in-house and to buy to fulfill the recent order at lowest possible cost. The model should meet or exceed the number of slip rings ordered of each type while using no more than the amount of wiring and harnessing capacity available. Do not constrain the decision variables to be integers.

2). Show how the optimal solution and its total cost change as the harnessing time required per Type C slip ring changes from 1 to 2.5 hours in increments of 0.25 hours. What is the relationship between total cost and harnessing time required per Type C slip ring (positive/negative, linear/nonlinear)?