The Mayflower Manufacturing Company produces a product on a number of machines

The Mayflower Manufacturing Company produces a product on a number of machines. When a machine breaks down, it must be repaired; and it takes one, either two or three days for the repair to be completed. Every time a machine breaks down, the cost to the company is an estimated R2 000 per day in lost production until the machine is repaired.

The company would like to know if it should implement a machine maintenance program at a cost of R20 000 per year that would reduce the frequency of breakdowns and thus the time for repair. The maintenance program would result in the following continuous probability function for time between breakdowns: