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Mathematics: Security Guards and Stolen Radios

Question: Twenty-first Century Electronics has discovered a theft problem at its warehouse and has decided to hire security guards. The firm wants to hire the optimal number of security guards. The following table shows how the number of security guards affects the number of guards affects the number of radios stolen per week.

Number of security guard Number of radios stolen per week
0 50
1 30
2 20
3 14
4 8
5 6
Questions:
1) If each security guard is paid $200 a week at the cost of a stolen radio is $25, how many security guards should the firm hire?
2) If the cost of a stolen radio is $25, what is the most a firm is willing to pay to hire the first security guard?
3) If each security guard is paid $200 a week and the cost of a stolen radio is $50, how many security guards should the firm hire?

Solution Preview

If each ratio is 25, then we can see that:

- hiring the first guard saves 20 radios (or $500),
- hiring the second guard saves 10 radios (or ($250)
- hiring the third guard saves 6 radios (or $150).

Since ...

Solution Summary

This solution provides a detailed, step by step response which illustrates how to determine the number of guards which are necessary in each case to prevent radio theft. All calculations are outlined in this response which is about 160 words.

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