Suppose a firm must employ 20 workers in order to produce 2,000 units of output that the firm has contracted to supply to the government for $1.4 million. The firm must choose how much to invest in...

Suppose a firm must employ 20 workers in order to produce 2,000 units of output that the firm has contracted to supply to the government for $1.4 million. The firm must choose how much to invest in safety. The firm can choose any level of safety, S, from 0 to 100. The cost of safety is C( S) = 50S². Given the firm’s choice of safety, the annual salary paid to workers is determined by
Annual salary = 60,000 - 300S
Thus, a firm that chooses S = 30 pays $45,000 for this level of safety and pays each worker $51,000. What level of safety will the firm choose, and how much does this cost? How much will each worker earn? How much profit will the firm earn?