Mamma Temte bakes six pies a day that cost $2 each to produce. On 15% of the days, she sells only two pies. On 27% of the days, she sells 4 pies, and on the remaining 58% of the days, she sells all six pies. If Mamma Temte sells her pies for $4 each, what is her expected profit for a day's worth of pies? ( Assume that any left over pies are given away).
To calculate Mamma Temte's expected profit for a day's worth of pies, we need to consider the number of pies she sells on each type of day and calculate the profit for each scenario.
1. On 15% of the days, Mamma Temte sells only 2 pies. In this case, her revenue would be $4 x 2 = $8. Each pie costs $2 to produce, so her cost for these 2 pies would be $2 x 2 = $4. Therefore, her profit for these days would be $8 - $4 = $4.
2. On 27% of the days, Mamma Temte sells 4 pies. The revenue would be $4 x 4 = $16, and the cost of producing these pies would be $2 x 4 = $8. So her profit for these days would be $16 - $8 = $8.
3. On the remaining 58% of the days, Mamma Temte sells all 6 pies. The revenue would be $4 x 6 = $24, and the cost of production would be $2 x 6 = $12. Hence, her profit for these days would be $24 - $12 = $12.
To calculate the expected profit, we need to multiply each profit by its corresponding probability and sum them up. Let's calculate it:
Expected Profit = (15% x $4) + (27% x $8) + (58% x $12)
Expected Profit = (0.15 x $4) + (0.27 x $8) + (0.58 x $12)
Expected Profit = $0.60 + $2.16 + $6.96
Expected Profit = $9.72
Therefore, Mamma Temte's expected profit for a day's worth of pies is $9.72.