dee is ian making Consider a three product firm facing a constrained linear technology. The firm is organized into two departments, machining and assembly. Machine hours are eonstraining in the first department and labor hours are eonstraining in the second department. The required machine and labor times for each product are listed below:

hours of machine time in department #1 hours of direct labor in department #2 product 1 product 2 product 3 1 2 3 2 4 5 Thus, eaeh unit of product #1 requires 1 machine hour in department #1 and 2 direet labor hours in department #2, and so on. Total capacity is 12,000 machine hours in department #1 and 15,000 direet labor hours in department #2.

Total manufacturing eost, for any feasible production plan q = (ql'C12,~), is given by TMC = 200,000 + 18ql + 24C12 + 45~. Respective selling prices are 130, 145, and 185 per unit.

The only period cost is specialized shipping "foam" that protects each of the products. This "foam" is purchased from a local suppIier at a cost of 100 perpound.

Each unit of product 1 requires .3 pounds of foam, each unit of product 2 requires

.5 pounds of foam, and each unit of product 3 requires .7 pounds of foam.

a] Formulate a linear program to maxirnize the firm's profit. Use four decision variables in your formulatioo, qj' q2' ~, and F (the total quantity of foam purchased).

Your LP should have three capacity eonstraints, dealing with total machine hours in department #1, total direct labor hours in department #2, and total foam eonsumed.

b] Without solving the LP, what is the shadow price on the foam eonstraint?

Carefully explain your reasoning. Then solve your LP and verify your conjecture.

e] Fonnulate a linear program to maximize the finn's profit using three decision variabies, ql, Is eost allocation involved?AppendixLO1