21st 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 guards. The follwoign table shows how the number of security guards affects the number of radios stolen each week:

Question

# of guards # of radios stolen per wk
0 50
1 30
2 20
3 14
4 8
5 6

a) If each security guards is paid
$200 a week and the cost of a
stolen radio is $25, how many
security guards shoudl the firm
hire?
b) If the cost of a stolen radio is
$25, what is the most the firm
would be willing to pay to hire the
first security guard?
c) If each security guard is paid $200
a week, and the cost of a stolen
radio is $50, how many guards
should the firm hire?

First, determine the marginal change in radios saved with each guard. Going from 0 to 1, the number of stolen radios goes from 50 to 30; ergo the marginal change is 20. Going from 1 to 2, the marginal change in radios is 10. Continue this with each additional guard.

a) the marginal number of radios saved would need to be 8 or greater.
b) the first security guard saves 20 radios, at $25 each, the firm would pay up to $500 for a guard.
c) take it from here.

Answer 1

The marginal number of radios saved would need to be 4 or greater.