Question

Great Southern Consultants Group's computer system has been down several times over the past few months, as shown below. Number of breakdowns 0 1 2 3 4 Monthly frequency 9 2 4 4 1 Each time the system is down, the firm loses an average of $400 in time and service expenses. They are considering signing a contract for preventive maintenance. With preventive maintenance, the system would be down on average only 0.5 per month. The monthly cost of preventive maintenance would be $200 a month. Which is cheaper, breakdown or preventive maintenance?

Answer 1

The expected monthly cost of breakdowns for Great Southern Consultants Group is $520, calculated based on the frequency and average loss per breakdown. Preventive maintenance costs $200 per month, making it the cheaper option compared to the losses incurred from system breakdowns.

Step-by-step explanation:

To determine which option is cheaper for Great Southern Consultants Group—breakdowns or preventive maintenance—we need to calculate the average cost of breakdowns and compare it to the cost of preventive maintenance. Based on the frequency distribution provided, the expected number of breakdowns per month can be calculated using the weighted average (also known as the expected value in probability and statistics), which is the sum of each number of breakdowns multiplied by its respective frequency, divided by the total number of months.

Let’s calculate the expected number of breakdowns per month:

(0×9) + (1×2) + (2×4) + (3×4) + (4×1) = 0 + 2 + 8 + 12 + 4 = 26 breakdowns.

Now we divide this by the total number of months: 26 breakdowns / 20 months = 1.3 breakdowns per month on average.

Now, we calculate the average monthly cost of breakdowns: 1.3 breakdowns/month × $400/breakdown = $520 per month. Therefore, preventive maintenance is cheaper since it would cost $200 per month, as opposed to the $520 per month cost of breakdowns without the contract.

The cost of preventive maintenance should be factored into the budget for the company as it appears to provide a cost saving when compared to the losses incurred from system breakdowns. We make this determination by analyzing the average monthly costs of both scenarios, and it is clear that the preventive maintenance option is more economical for the company.

Answer 2

- Preventive Maintenance

Step-by-step explanation:

Given that,

No. of breakdowns 0 1 2 3 4

Frequency 9 2 4 4 1

So,

No. of breakdowns Monthly probability

0 0.45

1 0.10

2 0.20

3 0.20

4 0.05

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Total 1.00

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As per the above data,

The breakdowns expected every month = (0 * 0.45) + (1 * 0.10) + (2 * 0.20) + (3 * 0.20) + (4 * 0.05)

= 1.30

∵ The cost expected for the breakdowns every month = 1.30 * $400

= $ 520

Now,

Per month cost of preventive maintenance = (0.5 * $400) + $200

= $ 400

Thus, preventive maintenance would be more economical.