A baker makes 500 cream-filled eclairs at a cost of $0.72 each. He estimates that 10% of the eclairs will be sold the following day at a reduced price of $0.80 each. Find the marked price if the baker wishes to obtain a 75% markup on cost.
A. $1.27
B. $1.31
C. $1.33
D. $1.45
A
To find the marked price that will give the baker a 75% markup on cost, we need to calculate the cost of each eclair and then add 75% to it.
1. Calculate the cost of each eclair:
The baker makes 500 cream-filled eclairs at a cost of $0.72 each. Therefore, the total cost of making 500 eclairs is 500 * $0.72 = $360.
2. Calculate the selling price of the 10% of eclairs that will be sold the following day at a reduced price of $0.80 each:
Since 10% of the eclairs will be sold the following day, the quantity of eclairs sold at $0.80 each will be 10% of 500, which is 0.10 * 500 = 50 eclairs.
Therefore, the revenue from selling these eclairs will be 50 * $0.80 = $40.
3. Calculate the remaining eclairs that will be sold at the marked price:
The remaining eclairs are 500 - 50 = 450 eclairs.
So, the revenue from selling these eclairs should be $360 + $40 = $400.
4. Calculate the total revenue required to obtain a 75% markup on cost:
The cost of producing 500 eclairs is $360, and to obtain a 75% markup, the total revenue should be $360 + 75% of $360.
Therefore, the total revenue required is $360 + (0.75 * $360) = $360 + $270 = $630.
5. Calculate the marked price:
The marked price is the selling price required to achieve a revenue of $630 for the 500 eclairs.
Therefore, the marked price per eclair is $630 / 500 = $1.26 per eclair.
Among the given options, the closest marked price is $1.27. Therefore, the correct answer is A. $1.27.