Question

a. Clean Water Company has been supplying treated water to a rural resort for the last 10 ast 24 months, the pumps have broken down at the rate indicated years. However, for the p in the table below: Number of Breakdowns Number of Months that Breakdown occurred 10 3 4 Total Each time the pumps breakdown, estimated losses is $2800. Alternatively, preventive per month. It is that the pumps may still breakdown on average once a month even with the monthly maintenance services may be outsourced at a contract price of $1200 scheduled maintenance. i. Compute the expe cted number of breakdowns if Clean Water continues to operate as it is (1.5 marks,) without the maintenance contract.

Answer 1

Answer:

Basic calculations as shown in the table above:

• Let no. of breakdown (first column) be A
• Let No. of months in which that no. of breakdown occurs be B
• Then total no of break downs in those months = C= A$\times$B
• Let cost of break down be D (D=2800)
• Then Total cost for those breakdowns(C). = E = C$\times$D
• Sum of E for all the no. of breakdown options( 0,1,2,3,4) is the total cost incurred due to all the breakdown in previous 24 months , Total cost =$112000.
• Similarly Sum of all the C, is the total no of breakdowns in previous 24 months.

Total no breakdowns= 40

??Part : 1

• Expected no. of breakdowns = average no of breakdown in previous 24 months = total breakdown/24
• Expected no of breakdown without contract= 40/24 = 1.66 breakdowns/month (Answer part1)

Part: 2

• Expected breakdowns per month = 1.66
• Cost per breakdown = $2800
• Total cost for breakdowns = cost per breakdown $\times$ expected no of break down
• Breakdown cost per month without contract = 2800$\times$1.66 = $4,648 (Answer for part B)

Part: 3

?Calculating cost for maintained contract:

• Total monthly cost with contract = monthly contract cost + monthly breakdown cost with contract
• Monthly contract cost = $1200
• No. of break downs per month with contract = 1
• Cost of breakdown per month with contract = 1 $\times$ 2800 = $2800
• Total monthly cost with maintenance = 2800 + 1200 = $4,000 (Answer to part-3)

Decision: Since the cost with preventive maintenance ($4000) is lesser than without it ($4648). So they should go with taking the preventive maintenance contract.