Linear Programming: The Random Company manufactures two products, Zeta and Beta. Each product must pass through two processing operations. All materials are introduced at the start of process no. I. There are no work in process inventories. Random may produce either one product exclusively or various combinations of both products subject to the following constraints:

A shortage of technical labor has limited Beta production to 400 units per day. There are no constraints on the production of Zeta other than the hour constraints in the above schedule. Assume that all relationships between capacity and production are linear.

Required:

a. Given the objective to maximize total contribution margin, what is the production constraint for process no. 1?

b. Given the objective to maximize total contribution margin, what is the labor constraint for production of Beta?

c. What is the objective function of the data presented?

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Process Number 1 Process Number 2 Contribution Margin per Unit Hours required to produce one unit of: Zeta Beta Total capacity in hours per day 1 hour 2 hours 1,000 hours 1 hour 3 hour 1,275 hours $4.00 5.25