Question: Consider the following short-run function for Superfast Hairdryers, Inc., given as:

Q = 10X- .25X²; where X is material inputs and Q is the output.

Suppose the hair dryers are sold for $10 per unit to K-Mart and that the firm can obtain as much of the variable materials (input X) as it needs at $20 per unit.

a. Write is the rule for determining the optimal units of input X?

b. Determine the marginal revenue product of X, given the above information.

c. Determine the marginal factor cost of X.

d. Determine the optimal value of X, given the objective function is to maximize profits.

e. If the price of hair dryers were to rise, what happens the optimal value of X employed to produce them?