Company X has discovered a theft problem at its warehouse and has decided to hir

Question

Company X has discovered a theft problem at its warehouse and has decided to hire security gaurds. The firm want to hire the optimal number of security gaurds. The following information shows how the number of gaurds affects the number of radios stolen per week:

0 gaurds, 50 stolen radios per week
1 gaurds, 30stolen radios per week
2 gaurds, 20 stolen radios per week
3 gaurds, 14 stolen radios per week
4 gaurds, 8 stolen radios per week
5 gaurds, 6 stolen radios per week

If each gaurd is paid $200/week, and a radio costs $25, how many security gaurds should the firm hire?

If the cost of a stolen radio is $25, what is the most a firm would pay to hire the first gaurd?

Explanation / Answer

The first guard costs 200 dollars and saves 50-30=20 radios per week radios cost 25$ each, hence the first guard saves 20*25$=500$ Since his wage (200) is less than the value of the radios saved (500), he will be employed. The second guard save 30-20=10 radios per week, which cost 10*25=250$ Since his wage (200) is less than the value of the radios saved (250), he will be employed. The third guard saves 20-14=6 radios per week which cost 6*25=150$. Since his wage (200) is more than the value of the radios saved (150), he will not be employed. --> the company will employ 2 guards. For the company to be better off, the cost of the guard has to be less than the value of the radios saved. The first guard saves 500 dollars worth in radios. Hence the company would be willing to pay him 499$.

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