A service that repairs TV's and sell maintenance agreement for $9 a yr. the average cost for repairing a TV is $39 and 3 in every 100 people who purchased maintenance agreements have TV that require repair
Find the services expected profit per maintenance agreement
prob(repair) = 3/100
expected cost = (3/100)($39) = $1.17
cost of agreement = $9.00
so profit per agreement = 7.83
Percentage of profit = 7.83/9 = .87 or 87%
(not bad, that is why I never buy these agreements)
another way to look at it.
Suppose 100 people bought the agreement
so they took in $900
but only 3 needed repairs, so the were out by $117
which is still a profit of $783
which is a percentage of 783/900 = .87 or 87%
To find the expected profit per maintenance agreement, we need to calculate the average profit per agreement.
Let's break down the information given:
- Price of maintenance agreement = $9 per year
- Average cost for repairing a TV = $39
- 3 out of every 100 people who purchased maintenance agreements require TV repair
First, let's calculate the revenue earned per maintenance agreement:
Revenue = Price of maintenance agreement = $9
Now, let's calculate the expected cost of repair for each agreement:
The probability that a TV requires repair = 3/100 = 0.03 (or 3%)
Cost of repair = Average cost for repairing a TV = $39
Expected cost of repair per maintenance agreement = Probability of repair × Cost of repair
= 0.03 × $39 = $1.17
Finally, let's calculate the expected profit per maintenance agreement:
Expected profit = Revenue - Cost of repair
= $9 - $1.17
= $7.83
Therefore, the expected profit per maintenance agreement is $7.83.
To find the service's expected profit per maintenance agreement, we need to calculate the annual income and expenses associated with the maintenance agreements.
Let's break down the calculations step by step:
1. Annual income from maintenance agreements:
The service sells maintenance agreements for $9 per year.
So, the annual income per maintenance agreement is $9.
2. Annual expenses for repairing TVs:
Given that 3 out of every 100 people who purchased maintenance agreements require TV repair, we can calculate the number of repairs per maintenance agreement as follows:
Number of repairs per maintenance agreement = (3/100) * 1
= 0.03 TV repairs
The average cost for repairing a TV is $39 per repair.
Therefore, the annual expenses for repairing TVs per maintenance agreement can be calculated as:
Annual expenses per maintenance agreement = Number of repairs per maintenance agreement * Average cost per repair
= 0.03 * $39
3. Expected profit per maintenance agreement:
The profit is calculated by subtracting the annual expenses from the annual income:
Expected profit per maintenance agreement = Annual income per maintenance agreement - Annual expenses per maintenance agreement
Substituting the values we calculated:
Expected profit per maintenance agreement = $9 - (0.03 * $39)
Performing the calculation:
Expected profit per maintenance agreement = $9 - $1.17
= $7.83
Therefore, the service's expected profit per maintenance agreement is $7.83.