ANSWER THIS QUESTION

A firm uses capital and labour to produce widgets. In the short-run capital is fixed, while labour is variable. The short-run production function is

X=-L3 + 24L2 + 240L

Where X is the number of widgets produced in per week, and L is the number of workers employed. Each worker works a 40-hour week. The wage rate is $12 per hour.

a. Calculate the range of values for L over which the firm is in stage I, stage II and stage III

b. what is the minimum product price at which the firm will operate in the short-run?

c. The product price, over which the firm has no control, is such that the firm's maximum possible pure profit $ 1096 per week. In order to achieve that level of profit it must employ 16 workers. How much is the firm's total fixed cost?.