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A pen manufacturer produces three types of pens: ballpoint pens, rollerball pens, and fountain pens. The company produces three variations of each type of pen, keeping the cost of production the same for each variation. The table gives the number of pens of each type sold.

\begin{tabular}{|l|c|c|c|}
\hline & Ballpoint & Rollerball & Fountain \\
\hline Variation 1 & 2,400 & 1,400 & 550 \\
\hline Variation 2 & 3,100 & 2,000 & 370 \\
\hline Variation 3 & 2,850 & 1,100 & 720 \\
\hline
\end{tabular}

The cost of production is \[tex]$1 per ballpoint pen, \$[/tex]2 per rollerball pen, and \[tex]$4 per fountain pen.

Calculate the total cost of production:

- Variation 1: \$[/tex] [tex]$\square$[/tex]
- Variation 2: \[tex]$ $[/tex]\square[tex]$
- Variation 3: \$[/tex] [tex]$\square$[/tex]

Sagot :

GinnyAnsweridn
Let's calculate the total cost of production for each variation of pens step-by-step, using the provided information.

### Variation 1
1. Ballpoint Pens:
- Number sold: 2400
- Cost per pen: [tex]$1 - Total cost for ballpoint pens = 2400 pens * $[/tex]1/pen = [tex]$2400 2. Rollerball Pens: - Number sold: 1400 - Cost per pen: $[/tex]2
- Total cost for rollerball pens = 1400 pens * [tex]$2/pen = $[/tex]2800

3. Fountain Pens:
- Number sold: 550
- Cost per pen: [tex]$4 - Total cost for fountain pens = 550 pens * $[/tex]4/pen = [tex]$2200 4. Total Cost for Variation 1: - Total cost = $[/tex]2400 (ballpoint) + [tex]$2800 (rollerball) + $[/tex]2200 (fountain) = [tex]$7400 ### Variation 2 1. Ballpoint Pens: - Number sold: 3100 - Cost per pen: $[/tex]1
- Total cost for ballpoint pens = 3100 pens * [tex]$1/pen = $[/tex]3100

2. Rollerball Pens:
- Number sold: 2000
- Cost per pen: [tex]$2 - Total cost for rollerball pens = 2000 pens * $[/tex]2/pen = [tex]$4000 3. Fountain Pens: - Number sold: 370 - Cost per pen: $[/tex]4
- Total cost for fountain pens = 370 pens * [tex]$4/pen = $[/tex]1480

4. Total Cost for Variation 2:
- Total cost = [tex]$3100 (ballpoint) + $[/tex]4000 (rollerball) + [tex]$1480 (fountain) = $[/tex]8580

### Variation 3
1. Ballpoint Pens:
- Number sold: 2850
- Cost per pen: [tex]$1 - Total cost for ballpoint pens = 2850 pens * $[/tex]1/pen = [tex]$2850 2. Rollerball Pens: - Number sold: 1100 - Cost per pen: $[/tex]2
- Total cost for rollerball pens = 1100 pens * [tex]$2/pen = $[/tex]2200

3. Fountain Pens:
- Number sold: 720
- Cost per pen: [tex]$4 - Total cost for fountain pens = 720 pens * $[/tex]4/pen = [tex]$2880 4. Total Cost for Variation 3: - Total cost = $[/tex]2850 (ballpoint) + [tex]$2200 (rollerball) + $[/tex]2880 (fountain) = [tex]$7930 ### Summary - The total cost of production for Variation 1 is $[/tex]7400.
- The total cost of production for Variation 2 is [tex]$8580. - The total cost of production for Variation 3 is $[/tex]7930.

Therefore, the results are:
- The total cost of production is [tex]$7400 for variation 1, $[/tex]8580 for variation 2, and $7930 for variation 3.
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