A firm produces cellular telephone service using equipment and labor. When it uses E machine-hours of equipment and hires L person-hours of labor, it can provide up to Q units 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?
b) What is the constraint?
c) Which of the variables (Q, E, L, PE, and PL) are exogenous? Which are endogenous? Explain.