Question

Math

Posted 3 months ago

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Manon's Ice Cream Shop sells only mint and raspberry ice cream. Each week, Manon puts either mint ice cream or raspberry ice cream on sale. She is trying to figure out which ice cream she should put on sale this week.
Manon gets all of her business from people who walk by her ice cream shop and stop in. She performs some market research and asks 1000 different people if they would purchase mint ice cream, raspberry ice cream, or no ice cream if they walked by and raspberry ice cream was on sale. She does the same for mint ice cream being on sale.
This week a total of 200 people will walk by Manon's Ice Cream Shop.
What is Manon's expected profit if she puts mint ice cream on sale? $\$$
$\square$
What is Manon's expected profit if she puts raspberry ice cream on sale? $\$$
$\square$
To maximize her expected profit, Manon should put $\square$ ice cream on sale.
(If necessary, round your answers to the nearest cent.)
The following table shows the profit for each type of ice cream depending on which ice cream Manon puts on sale.
\begin{tabular}{rcc}
& Mint on sale & Raspberry on sale \\
\hline Profit from mint & $\$ 3.00$ & $\$ 4.00$ \\
Profit from raspberry & $\$ 3.00$ & $\$ 2.50$
\end{tabular}
The following table shows the results from her market research.
\begin{tabular}{ccc}
Customer choice & Mint on sale & Raspberry on sale \\
\hline Mint & 305 & 219 \\
Raspberry & 314 & 501 \\
No ice cream & 381 & 280 \\
Total & 1000 & 1000
\end{tabular}
```

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Answer from Sia

Posted 3 months ago

Solution by Steps

step 1

Calculate the expected number of customers choosing mint when mint is on sale: $(305/1000) \times 200$

step 2

Calculate the expected number of customers choosing raspberry when mint is on sale: $(314/1000) \times 200$

step 3

Calculate the expected profit from mint when mint is on sale: $(305/1000 \times 200) \times 3$

step 4

Calculate the expected profit from raspberry when mint is on sale: $(314/1000 \times 200) \times 3$

step 5

Add the expected profits from mint and raspberry to find the total expected profit when mint is on sale: $((305/1000 \times 200) \times 3) + ((314/1000 \times 200) \times 3)$

step 6

Use the asksia-ll calculation list to find the total expected profit when mint is on sale: $371.4$

1 Answer

$371.4

step 7

Calculate the expected number of customers choosing mint when raspberry is on sale: $(219/1000) \times 200$

step 8

Calculate the expected number of customers choosing raspberry when raspberry is on sale: $(501/1000) \times 200$

step 9

Calculate the expected profit from mint when raspberry is on sale: $(219/1000 \times 200) \times 4$

step 10

Calculate the expected profit from raspberry when raspberry is on sale: $(501/1000 \times 200) \times 2.5$

step 11

Add the expected profits from mint and raspberry to find the total expected profit when raspberry is on sale: $((219/1000 \times 200) \times 4) + ((501/1000 \times 200) \times 2.5)$

step 12

Use the asksia-ll calculation list to find the total expected profit when raspberry is on sale: $425.7$

2 Answer

$425.7

step 13

Compare the total expected profits from both scenarios to determine which flavor Manon should put on sale to maximize profit

3 Answer

Manon should put raspberry ice cream on sale to maximize her expected profit.

Key Concept

Expected Profit Calculation

Explanation

The expected profit is calculated by multiplying the probability of each event (customer choice) by the profit associated with that event and summing these products for all events.

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