To calculate the manufacturer's profit from the warranties, we need to follow these steps:
- Calculate the total revenue from selling the warranties.
- Calculate the total cost associated with honoring 12% of the warranties.
- Subtract the total cost from the total revenue to find the profit.
Step 1: Calculate Total Revenue from Warranties
The price of each warranty is $225, and the manufacturer sold 532,475 warranties.
\[ \text{Total Revenue} = \text{Number of Warranties} \times \text{Price per Warranty} \]
\[ \text{Total Revenue} = 532,475 \times 225 \]
\[ \text{Total Revenue} = 119,836,875 \]
Step 2: Calculate Total Cost of Honoring Warranties
The manufacturer has to honor 12% of the warranties. First, we find out how many warranties are honored:
\[ \text{Warranties Honored} = 532,475 \times 0.12 \]
\[ \text{Warranties Honored} = 63,897 \]
Next, we calculate the total cost to honor these warranties, assuming each warranty costs $225:
\[ \text{Total Cost} = \text{Warranties Honored} \times \text{Cost per Warranty} \]
\[ \text{Total Cost} = 63,897 \times 225 \]
\[ \text{Total Cost} = 14,377,725 \]
Step 3: Calculate Profit from Warranties
Now we subtract the total cost from total revenue to find the profit:
\[ \text{Profit} = \text{Total Revenue} - \text{Total Cost} \]
\[ \text{Profit} = 119,836,875 - 14,377,725 \]
\[ \text{Profit} = 105,459,150 \]
Thus, the profit gained by the manufacturer from the warranties is approximately $105,459,150.
However, since none of the options (a, b, c, d) exactly match this amount, let's look for approximations based on the calculation. The option that is closest to this value is:
a. $105,430,050.
Hence, the correct answer is a.
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