Question

Mamma Temte bakes six pies a day that cost $2 each to produce. On 18% of the days she sells only two pies. On 26% of the days, she sells 4 pies, and on the remaining 56% of the days, she sells all six pies. If Mama Temte sells her pies for $4 each, what is her expected profit for a day’s worth of pies? {assume that the left over pies are given away.

Answer 1

Mama Temte's expected profit for a day's sales of pies is calculated by considering different scenarios where she sells varying numbers of pies and their respective probabilities. By multiplying the profit of each scenario by their probability and summing up, we find the expected daily profit is $7.04.

Step-by-step explanation:

The question asks to calculate the expected profit for Mama Temte's pie sales. To find Mama Temte's expected daily profit, we can use probability and expected value calculations. Let's break down the profits based on scenarios, considering she bakes 6 pies every day at a cost of $2 each, hence a daily production cost of $12:

• On 18% of the days, she sells 2 pies at $4 each, so her revenue is 2 * $4 = $8. Profit for these days is $8 - $12 = -$4.
• On 26% of the days, she sells 4 pies at $4 each, so her revenue is 4 * $4 = $16. Profit for these days is $16 - $12 = $4.
• On 56% of the days, she sells all 6 pies at $4 each, so her revenue is 6 * $4 = $24. Profit for these days is $24 - $12 = $12.

Now we calculate the expected profit by multiplying the profit of each scenario by their respective probabilities and adding the results together:

1. 0.18 * (-$4) + 0.26 * $4 + 0.56 * $12
2. = -$0.72 + $1.04 + $6.72
3. = $7.04

Thus, Mama Temte's expected profit for a day's worth of pies is $7.04.