A Salesperson Works for a Car Dealership for 40 Hours

Multiple Choice

A salesperson works for a car dealership for 40 hours per week,but may choose not to work hard all of the time.The dealership's owner cannot observe the salesperson's effort,but can observe the number of cars sold.The salesperson's personal cost of working at the dealership is C(H) = 1,200 + H²,where H is the number of hours during which he works hard.The corresponding marginal cost of effort is MC = 2H.Without any effort,the salesperson will,on average,generate a profit of $1,200.With each hour of high effort,he has a 5 percent chance of selling a car.Each car sale generates a profit of $900.What is the efficient number of hours of hard work?

A) 22.5
B) 20
C) 40
D) 27.5