Answer to Question #119932 in Microeconomics for Rosi

Question

A firm produces cellular telephone service using equipment and labor. When it uses E machine-hours of equipment and hires L person-ours of labor, it can provide up to Q unites of telephone service. The relationship between Q, E, and L is as follows: Q = EL . The firm must always pay PE for each machine-hour of equipment it uses and PL for each person-hour of Labor it hires. Suppose the production manager is told to produce Q=200 units of telephone service and that she wants to choose E and L to minimize costs while achieving that production target.
a) What is the objective function for this problem?

Answer 1

Production function: Q(E,L)

Production function: Q = EL

Total cost: TC = PE + PL

To produce 200 units (Q = 200 units)

Objective: minimize cost: PE + PL = TC

Subject to: Q = 200