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Questions: Consider a ?rm that produces language learning instruction using equipment and labour. When it uses E machine-hours of equipment and hires L person-hours of labour, it can provide up to Q units of language instruction. The relationship between Q, E, and L is as follows: Q = x/F + x/L. The ?rm must always pay PE for each machine hour of equipment it uses and PL for each person-hour of labour it hires. Suppose the production manager is told to produce Q = 400 units of language learning 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.
d. Write a statement of the constrained optimization problem.
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