The following figure 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 figure 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

By looking at the chart, we can see that the addition of the first security guard results in a reduction of $60 in total losses due to theft. Adding a second security guard increases the reduction to $95, which is an increase of $35 from the first security guard. Adding a third security guard increases the reduction to $115, which is only a $20 increase from the second security guard. Adding a fourth security guard increases the reduction to $125, which is only a $10 increase from the third security guard. Adding a fifth or sixth security guard does not result in any additional reduction in total losses due to theft.

Therefore, the optimal number of security guards to hire is four, which would reduce total losses due to theft by a total of $265. Hiring additional guards beyond four would not result in a significant reduction in total losses due to theft, and would therefore be a waste of money.

To hire four security guards at $45 per day would cost the store $180 per day, but the reduction in total losses due to theft would be $265 per day. Therefore, it would be profitable for the store to hire four security guards.

The Following Figure Indicates the Reductions in Total Losses Due