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.
