To find the profit the manufacturer made from the warranties, we need to follow these steps:
- Calculate the total revenue from selling the warranties.
- Determine the total amount the manufacturer has to pay out for honoring the warranties.
- Subtract the total payout from the total revenue to find the profit.
Step 1: Total Revenue from Warranties
The cost of one warranty is $17. If the manufacturer sells 475,360 warranties, the total revenue from selling the warranties is: \[ \text{Total Revenue} = \text{Number of Warranties} \times \text{Cost per Warranty} \] \[ \text{Total Revenue} = 475,360 \times 17 \] \[ \text{Total Revenue} = 8,078,120 \]
Step 2: Total Payout for Warranties
The manufacturer has to honor 7.5% of the sold warranties. First, we calculate how many warranties will be honored: \[ \text{Warranties Honored} = 0.075 \times 475,360 \] \[ \text{Warranties Honored} = 35,152 \]
Now, we need to calculate the total amount the manufacturer has to pay out for these honored warranties. Assuming the cost of honoring a warranty is the same as the cost of the warranty ($17): \[ \text{Total Payout} = \text{Warranties Honored} \times \text{Cost per Warranty} \] \[ \text{Total Payout} = 35,152 \times 17 \] \[ \text{Total Payout} = 597,584 \]
Step 3: Profit Calculation
Now we can calculate the profit: \[ \text{Profit} = \text{Total Revenue} - \text{Total Payout} \] \[ \text{Profit} = 8,078,120 - 597,584 \] \[ \text{Profit} = 7,480,536 \]
Looking at the answer choices, the closest one is: \[ \text{b. } 7,475,036 \]
However, this number does not exactly match our calculation, but it is the nearest option based on the figures given.
Thus, the profit the manufacturer made from the warranties is: b. $7,475,036
1 answer