To find out how many phones ProPhone needs to sell to maximize profit, we need to calculate the profit at each level of quantity and then determine the quantity corresponding to the highest profit.
1. Calculate the Profit (or Loss) at Each Quantity Level:
Profit at each quantity level is given by the formula:
[tex]\[
\text{Profit} = \text{Total Revenue} - \text{Total Cost}
\][/tex]
Using the given data from the table:
- For Quantity 0:
[tex]\[
\text{Profit} = 0 - 90 = -90
\][/tex]
- For Quantity 1:
[tex]\[
\text{Profit} = 200 - 170 = 30
\][/tex]
- For Quantity 2:
[tex]\[
\text{Profit} = 360 - 200 = 160
\][/tex]
- For Quantity 3:
[tex]\[
\text{Profit} = 480 - 290 = 190
\][/tex]
- For Quantity 4:
[tex]\[
\text{Profit} = 600 - 340 = 260
\][/tex]
- For Quantity 5:
[tex]\[
\text{Profit} = 700 - 400 = 300
\][/tex]
- For Quantity 6:
[tex]\[
\text{Profit} = 810 - 500 = 310
\][/tex]
- For Quantity 7:
[tex]\[
\text{Profit} = 910 - 620 = 290
\][/tex]
2. Determine Which Quantity Yields the Maximum Profit:
From the calculated profits:
- Quantity 0: Profit = -90
- Quantity 1: Profit = 30
- Quantity 2: Profit = 160
- Quantity 3: Profit = 190
- Quantity 4: Profit = 260
- Quantity 5: Profit = 300
- Quantity 6: Profit = 310
- Quantity 7: Profit = 290
The highest profit, 310, occurs when the quantity sold is 6.
Therefore, ProPhone needs to sell six phones to maximize profit.
