Vaska Electronics has discovered a theft problem at its warehouse and has decided to hire some security guards. The following table shows the number of security guards and the amount of theft per week:
(#of security guards)(#of stolen radios)
0 50
1 30
2 20
3 14
4 8
5 6
The cost of stolen radio is $25 and a security guard costs $200 per week.
A) How many guards should Vaska Electronics hire?
B) What is the most that Vaska Electronics would be willing to pay for the first security guard?
C) Suppose the cost of a stolen radio is $50. How many security guards would Vaska Electronics hire if each security guard costs $200 per week?
A spreadsheet could do this easily.
Columns
#guards CostGuards StolenRad costrad Total cost
do that spreadsheet for guards 0 to 6, and compute total cost for each (total cost=costradiosstolen+ guardcost
It seems to me that some simple arithmetic will answer your questions.
A) To determine how many guards Vaska Electronics should hire, we need to analyze the relationship between the number of security guards and the amount of theft per week.
First, let's create a table to compare the weekly cost and the amount of theft:
(# of security guards) (# of stolen radios) (weekly cost) (theft cost) (total cost)
0 50 $0 $1250 $1250
1 30 $200 $750 $950
2 20 $400 $500 $900
3 14 $600 $350 $950
4 8 $800 $200 $1000
5 6 $1000 $150 $1150
The weekly cost is calculated by multiplying the number of security guards by $200 per guard. The theft cost is calculated by multiplying the number of stolen radios by $25 per radio. The total cost is the sum of the weekly cost and the theft cost.
Based on this analysis, Vaska Electronics should hire 2 security guards because this would result in the lowest total cost of $900 per week.
B) To determine the maximum amount Vaska Electronics would be willing to pay for the first security guard, we need to compare the cost of hiring a guard to the amount of theft prevented.
From the table above, we can see that with 1 security guard, Vaska Electronics experiences a weekly theft of 30 radios, resulting in a theft cost of $750. If we assume that hiring a guard eliminates all theft, the company would save $750 per week. Therefore, Vaska Electronics would be willing to pay up to $750 for the first security guard.
C) If the cost of a stolen radio is now $50, we can analyze the relationship between the number of security guards and the amount of theft, and determine the number of guards Vaska Electronics should hire.
Let's create a new table (similar to the one above) with a theft cost of $50 per radio:
(# of security guards) (# of stolen radios) (weekly cost) (theft cost) (total cost)
0 50 $0 $2500 $2500
1 30 $200 $1500 $1700
2 20 $400 $1000 $1400
3 14 $600 $700 $1300
4 8 $800 $400 $1200
5 6 $1000 $300 $1300
Based on this analysis, Vaska Electronics should hire 3 security guards because this would result in the lowest total cost of $1300 per week.