Answered

A local snow cone business sells snow cones in one size for [tex]$\$[/tex] 5$. It has the following cost and output structure per hour.

\begin{tabular}{|r|r|r|r|r|r|}
\hline
\begin{tabular}{c}
Output (cones per \\ hour)
\end{tabular} & Total Cost (per hour) & Total Revenue & Total Profit & Marginal Revenue & Marginal Cost \\
\hline
0 & 30 & & & & \\
\hline
10 & 75 & & & & \\
\hline
20 & 105 & & & & \\
\hline
30 & 125 & & & & \\
\hline
35 & 145 & & & & \\
\hline
40 & 170 & & & & \\
\hline
45 & 200 & & & & \\
\hline
50 & 250 & & & & \\
\hline
\end{tabular}

To maximize profit, the firm should produce how many snow cones per hour?

A. 25

B. 30

C. 35

D. 40



Answer :

GinnyAnswer
Let's analyze the problem step-by-step:

1. Output and Total Cost Information:
- Given the output (number of cones) and their respective total costs from the table:
- 10 cones: [tex]$\$[/tex]75[tex]$ - 20 cones: $[/tex]\[tex]$105$[/tex]
- 30 cones: [tex]$\$[/tex]125[tex]$ - 35 cones: $[/tex]\[tex]$145$[/tex]
- 40 cones: [tex]$\$[/tex]170[tex]$ - 45 cones: $[/tex]\[tex]$200$[/tex]
- 50 cones: [tex]$\$[/tex]250[tex]$ 2. Calculate Total Revenue: - Each cone sells for $[/tex]\[tex]$5$[/tex], so the total revenue can be computed as follows:
- 10 cones: [tex]\(10 \times 5 = \$50\)[/tex]
- 20 cones: [tex]\(20 \times 5 = \$100\)[/tex]
- 30 cones: [tex]\(30 \times 5 = \$150\)[/tex]
- 35 cones: [tex]\(35 \times 5 = \$175\)[/tex]
- 40 cones: [tex]\(40 \times 5 = \$200\)[/tex]
- 45 cones: [tex]\(45 \times 5 = \$225\)[/tex]
- 50 cones: [tex]\(50 \times 5 = \$250\)[/tex]

3. Calculate Total Profit:
- Total profit is computed as Total Revenue minus Total Cost:
- 10 cones: [tex]\( \$50 - \$75 = -\$25 \)[/tex]
- 20 cones: [tex]\( \$100 - \$105 = -\$5 \)[/tex]
- 30 cones: [tex]\( \$150 - \$125 = \$25 \)[/tex]
- 35 cones: [tex]\( \$175 - \$145 = \$30 \)[/tex]
- 40 cones: [tex]\( \$200 - \$170 = \$30 \)[/tex]
- 45 cones: [tex]\( \$225 - \$200 = \$25 \)[/tex]
- 50 cones: [tex]\( \$250 - \$250 = \$0 \)[/tex]

4. Marginal Revenue and Marginal Cost:
- Marginal revenue is constant at [tex]$\$[/tex]5[tex]$ per cone as the price per cone remains fixed. - Marginal cost is calculated as the change in total cost with each additional cone produced: - From 10 to 20 cones: \( \$[/tex]105 - \[tex]$75 = \$[/tex]30 \)
- From 20 to 30 cones: [tex]\( \$125 - \$105 = \$20 \)[/tex]
- From 30 to 35 cones: [tex]\( \$145 - \$125 = \$20 \)[/tex]
- From 35 to 40 cones: [tex]\( \$170 - \$145 = \$25 \)[/tex]
- From 40 to 45 cones: [tex]\( \$200 - \$170 = \$30 \)[/tex]
- From 45 to 50 cones: [tex]\( \$250 - \$200 = \$50 \)[/tex]

5. Identify the Quantity with the Highest Profit:
- Reviewing the total profit calculated earlier:
- Maximum profit occurs at 35 and 40 cones, where the profit is [tex]$\$[/tex]30$.

Therefore, to maximize profit, the firm should produce 35 snow cones per hour.