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\begin{tabular}{|c|c|c|c|}
\hline
\begin{tabular}{c}
Widgets \\
produced \\
per day
\end{tabular} & \begin{tabular}{c}
Total \\
cost
\end{tabular} & \begin{tabular}{c}
Marginal \\
revenue
\end{tabular} & Profit \\
\hline 1 & \[tex]$15 & \$[/tex]13 & -\[tex]$2 \\
\hline 2 & \$[/tex]18 & \[tex]$13 & \$[/tex]5 \\
\hline 3 & \[tex]$20 & \$[/tex]13 & \[tex]$19 \\
\hline 4 & \$[/tex]25 & \[tex]$13 & \$[/tex]27 \\
\hline 5 & \[tex]$35 & \$[/tex]13 & \[tex]$30 \\
\hline 6 & \$[/tex]48 & \[tex]$13 & \$[/tex]40 \\
\hline 7 & \[tex]$68 & \$[/tex]13 & \[tex]$23 \\
\hline
\end{tabular}

Use the table to answer the following questions:

1. The profit when the company makes five widgets is $[/tex]\square[tex]$.

2. To maximize profit, the company should produce $[/tex]\square[tex]$ widgets per day.

3. The company's profits would decrease by $[/tex]\square$ if the company made seven widgets.



Answer :

GinnyAnswer
Let's analyze the table given and answer the questions step-by-step:

1. Finding the profit when the company makes five widgets:
From the table, when the company produces 5 widgets, the profit is listed as \[tex]$30. Therefore, the profit when the company makes five widgets is \(\$[/tex]30\).

2. Finding the number of widgets to produce to maximize profit:
We look at the profit values listed in the table to find the maximum profit:
- For 1 widget: [tex]\(-\$2\)[/tex]
- For 2 widgets: \[tex]$5 - For 3 widgets: \$[/tex]19
- For 4 widgets: \[tex]$27 - For 5 widgets: \$[/tex]30
- For 6 widgets: \[tex]$40 - For 7 widgets: \$[/tex]23

The maximum profit of \[tex]$40 occurs when the company produces 6 widgets. Therefore, to maximize profit, the company should produce \(6\) widgets per day. 3. Calculating the decrease in profit if the company made seven widgets instead of six: - Profit for 6 widgets: \$[/tex]40
- Profit for 7 widgets: \[tex]$23 The decrease in profit if the company made seven widgets instead of six is calculated as: \[ \text{Decrease in profit} = \text{Profit for 6 widgets} - \text{Profit for 7 widgets} = \$[/tex]40 - \[tex]$23 = \$[/tex]17
\]
Therefore, the company's profits would decrease by [tex]\(\$17\)[/tex] if the company made seven widgets.

Putting it all together, we have:
- The profit when the company makes five widgets is [tex]\(\$30\)[/tex].
- To maximize profit, the company should produce [tex]\(6\)[/tex] widgets per day.
- The company's profits would decrease by [tex]\(\$17\)[/tex] if the company made seven widgets.

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