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
2pies *15% +4pies * 27% + 6 pies *58
2(.15)+4(.27)+ 6(.58) = 4.86 pies
Profit = $4(4.86) - $2(6)
Profit = $19.44 - $12 = $ 7.44
Well, it seems like Mamma Temte is really putting the "pie" in profit! Let's crunch some numbers here:
First, let's calculate the number of days she sells two pies. 15% of the time that Mamma Temte sells pies, she sells only two. With six pies in total, that's (15/100) * 6 = 0.15 * 6 = 0.9 pies sold. Since we can't sell a fraction of a pie, she sells 0 pies on those days.
Next up, she sells four pies on 27% of the days. Using the same math, (27/100) * 6 = 1.62 pies sold. Again, let's round it down to 1 piece of pie sold.
Lastly, she sells all six pies on the remaining 58% of the days. This is straightforward, as she sells all of them, so she sells 6 pies on those days.
Now, let's calculate her total profit. Each pie costs $2 to produce, and she sells them for $4 each. So, her profit per pie is $4 - $2 = $2.
On the days she sells 0 pies, her profit is $2 * 0 pies = $0.
On the days she sells 1 pie, her profit is $2 * 1 pie = $2.
On the days she sells 6 pies, her profit is $2 * 6 pies = $12.
Adding it all up, her total expected profit for a day's worth of pies is $0 + $2 + $12 = $14.
So there you have it! Mamma Temte can expect to make a profit of $14 for a day's worth of pies. That's a lot of dough!
To determine Mamma Temte's expected profit, we need to calculate the profit for each scenario and then take the weighted average.
First, let's calculate the profit for each scenario:
1. On 15% of the days, she sells only two pies.
Profit = ($4 - $2) * 2 = $4
2. On 27% of the days, she sells 4 pies.
Profit = ($4 - $2) * 4 = $8
3. On the remaining 58% of the days, she sells all six pies.
Profit = ($4 - $2) * 6 = $12
Next, let's calculate the weighted average by considering the percentages of each scenario:
Weighted average profit = (15% * $4) + (27% * $8) + (58% * $12)
Weighted average profit = (0.15 * 4) + (0.27 * 8) + (0.58 * 12)
Weighted average profit = $0.6 + $2.16 + $6.96
Weighted average profit = $9.72
Therefore, Mamma Temte's expected profit for a day's worth of pies is $9.72.
To find Mamma Temte's expected profit for a day's worth of pies, we need to calculate the profit for each possible number of pies sold and then multiply it by the respective probability of that number of pies being sold.
Let's start by calculating the profit for each scenario:
1) On 15% of the days, Mamma Temte sells only two pies.
Profit from selling 2 pies = (Selling price - Cost) x Number of pies
Profit from selling 2 pies = ($4 - $2) x 2 = $4
2) On 27% of the days, Mamma Temte sells 4 pies.
Profit from selling 4 pies = (Selling price - Cost) x Number of pies
Profit from selling 4 pies = ($4 - $2) x 4 = $8
3) On the remaining 58% of the days, Mamma Temte sells all six pies.
Profit from selling 6 pies = (Selling price - Cost) x Number of pies
Profit from selling 6 pies = ($4 - $2) x 6 = $12
Now let's calculate the expected profit by multiplying each scenario's profit by its respective probability:
Expected profit = (Profit from 2 pies x Probability of selling 2 pies) + (Profit from 4 pies x Probability of selling 4 pies) + (Profit from 6 pies x Probability of selling 6 pies)
Expected profit = ($4 x 0.15) + ($8 x 0.27) + ($12 x 0.58)
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.