decision making with reciprocal allocation Ralph is now managing a finn with interdependent service eeJlters. Two such centers are involved, say, power and maintenance. For eaeh such center, 80% of total output goes to manufacturing and 20% goes to the other service center. The variable eost of power is 10 per unit while the variable eost of maintenance is 15 per unit. Produetion requires 800 units of eaeh service. Hence, 1,000 (gross) units of eaeh are produced at a total variable eost of 25,000.

Ralph is eonsidering an opportunity to purchase power (all or some) from an outside vendor, and the following questions are to be answered with this in mind.
a] What is the eost per unit of power? (Hint: use the simultaneous equation method of allocation.)
b] Now formulate and solve a linear program to determine the minimum eost aetivity level s for power and maintenanee in order to provide manufaeturing with at least 800 units of eaeh serviee. You ean infer from the noted produetion plan that eaeh unit of power requires .2 units of maintenanee and viee versa. So the technieal eonstraints in your LP should be P - .2M :2: 800 and M - .2P :2: 800, where P denotes units of power and M denotes units of maintenanee.
e] Compare your eost per unit of power in [a] above with the shadow priee on the power eonstraint in [bl above. Carefully explain why they differ, if the differ, of why they are the same ifthey are the same. (13.5417 should be a familiar number.)
d] Suppose the outside source wiII sell power at 12 per unit. Should this offer be accepted? If so, determine the total saving.
e] Finally, formulate and solve an LP related to that in Ib] above but with a third variable, x, units of power purehased from the outside souree at 12 per unit.
f] In part [d] above you used a eost of internai power of 13.5417 to answer the sourcing question, but in the LP in [e] you used a eost of internai power of 10.00 per unit to answer the sourcing question. Carefully explain.AppendixLO1