The following chart indicates the reductions in total losses due to theft if a jewelry store hires additional security guards.

If the security guards can be hired for $45 per day, how many guards should the shop hire?

Question

The following chart indicates the reductions in total losses due to theft if a jewelry store hires additional security guards.

If the security guards can be hired for $45 per day, how many guards should the shop hire?

Quizplus · Accepted Answer

From the chart, we can see that the addition of each security guard results in a decrease in total losses due to theft. The first security guard reduces losses by $100, the second by $200, the third by $250, the fourth by $275, and the fifth by $280.

To determine the cost-effectiveness of each guard, we need to calculate the cost of hiring each guard and divide it by the reduction in losses that they provide.

The cost of hiring each guard for a day is $45, so the cost of hiring n guards for a day is 45n.

If we divide the cost of adding each guard by the reduction in total losses due to theft, we get the following:

- Guard 1: Cost = $45, Loss Reduction = $100, Cost-Reduction Ratio = 0.45
- Guard 2: Cost = $90, Loss Reduction = $200, Cost-Reduction Ratio = 0.45
- Guard 3: Cost = $135, Loss Reduction = $250, Cost-Reduction Ratio = 0.54
- Guard 4: Cost = $180, Loss Reduction = $275, Cost-Reduction Ratio = 0.65
- Guard 5: Cost = $225, Loss Reduction = $280, Cost-Reduction Ratio = 0.80

Based on this analysis, we can see that the cost-reduction ratio increases up to the fourth guard, so hiring four security guards would be the most cost-effective option, resulting in a total cost of $180 for a reduction in total losses of $825. Therefore, the answer is C) 4.

The Following Chart Indicates the Reductions in Total Losses Due