DuLarge Marine manufactures diesel engines for shrimp trawlers and other small commercial boats. One of their CNC machines, which is used $50$ weeks in a year, has caused several problems. Over the past $30$ weeks, the machine has broken down as indicated below. Each time the machine breaks down, the firm loses an average of $$3,000$ in time and repair expenses. If preventive maintenance were implemented, it is estimated that an average of only one breakdown per week would occur. The cost of preventive maintenance is $$1,000$ per week. $($Hint: compute Total first$).$

Number of breakdowns per week

$0$

$1$

$2$

$3$

$4$

Total

Frequency

$8$

$3$

$5$

$9$

$5$

x

What is the expected yearly total maintenance cost of this preventive program?

A$.$

$$80,000$

B$.$

$$15,000$

C$.$

$$20,000$

D$.$

$$6,600$

E$.$

$$4,000$