Suppose Sarah owns a small company that makes wedding cakes. The accompanying table shows how Sarah's total cost varies depending on the number of wedding cakes she makes each day. $$\begin{array} { | c | c | }
\hline \text { Number of Cales Per Day } & \text { Tatal Cast Per Day } \
\hline 0 & \$ 100 \
\hline 1 & \$ 180 \
\hline 2 & \$ 220 \
\hline 3 & \$ 300 \
\hline 4 & \$ 400 \
\hline 5 & \$ 520 \
\hline 6 & \$ 660 \
\hline
\end{array}$$
If the market for wedding cakes is perfectly competitive, and wedding cakes sell for $125 each, then at her profit-maximizing level of output, Sarah's profit will be ________ per day.

Question

Suppose Sarah owns a small company that makes wedding cakes. The accompanying table shows how Sarah's total cost varies depending on the number of wedding cakes she makes each day. $$\begin{array} { | c | c | } 
\hline \text { Number of Cales Per Day } & \text { Tatal Cast Per Day } \
\hline 0 & \$ 100 \
\hline 1 & \$ 180 \
\hline 2 & \$ 220 \
\hline 3 & \$ 300 \
\hline 4 & \$ 400 \
\hline 5 & \$ 520 \
\hline 6 & \$ 660 \
\hline
\end{array}$$  
If the market for wedding cakes is perfectly competitive, and wedding cakes sell for $125 each, then at her profit-maximizing level of output, Sarah's profit will be ________ per day.

Quizplus · Accepted Answer

To find the profit-maximizing level of output, we calculate the profit for each level of output and choose the highest profit. Profit is calculated as (Price per cake * Number of cakes) - Total Cost. For each level of output: - 0 cakes: Profit = $(125*0) - $100 = -$100 - 1 cake: Profit = $(125*1) - $180 = -$55 - 2 cakes: Profit = $(125*2) - $220 = $30 - 3 cakes: Profit = $(125*3) - $300 = $75 - 4 cakes: Profit = $(125*4) - $400 = $100 - 5 cakes: Profit = $(125*5) - $520 = $105 (highest profit) - 6 cakes: Profit = $(125*6) - $660 = $90 The highest profit is $105, achieved by selling 5 cakes.

Suppose Sarah Owns a Small Company That Makes Wedding Cakes