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Cost Equation:
- The fixed costs per week: [tex]$100
- The cost to produce each item: $[/tex]2 per item

Cost Equation in Slope-Intercept Form:
[tex]\[ y = 2x + 100 \][/tex]

Revenue Equation:
- Selling price per item: [tex]$15

\ \textless \ strong\ \textgreater \ Revenue Equation in Slope-Intercept Form:\ \textless \ /strong\ \textgreater \
\[ y = 15x \]

\ \textless \ strong\ \textgreater \ Calculation for 10 items:\ \textless \ /strong\ \textgreater \
1. \ \textless \ strong\ \textgreater \ Total Costs:\ \textless \ /strong\ \textgreater \
\[ \text{Cost} = 2(10) + 100 = 20 + 100 = 120 \]

2. \ \textless \ strong\ \textgreater \ Revenue:\ \textless \ /strong\ \textgreater \
\[ \text{Revenue} = 15(10) = 150 \]

3. \ \textless \ strong\ \textgreater \ Profit:\ \textless \ /strong\ \textgreater \
\[ \text{Profit} = \text{Revenue} - \text{Cost} = 150 - 120 = 30 \]

\ \textless \ strong\ \textgreater \ Summary:\ \textless \ /strong\ \textgreater \
- Cost Equation: \( y = 2x + 100 \)
- Revenue Equation: \( y = 15x \)
- Total Costs for 10 items: \( \$[/tex]120 \)
- Revenue from selling 10 items: [tex]\( \$150 \)[/tex]
- Profit: [tex]\( \$30 \)[/tex]

Sagot :

GinnyAnsweridn
Let's carefully go through each part of the problem, step-by-step.

1. Cost Equation:

Given:
- Fixed costs per week: \[tex]$100 - Variable cost per item: \$[/tex]2 per item

The total cost is the sum of the fixed costs and the variable costs, which can be written as:
[tex]\[ y = 100 + 2x \][/tex]

So, the cost equation in the slope-intercept form is:
[tex]\[ y = 100 + 2x \][/tex]

2. Revenue Equation:

Given:
- Selling price per item: \[tex]$15 The total revenue is the selling price multiplied by the number of items sold, which can be written as: \[ y = 15x \] So, the revenue equation in the slope-intercept form is: \[ y = 15x \] 3. Total Costs When 10 Items Are Made: The number of items produced and sold this week: \( x = 10 \) Using the cost equation \( y = 100 + 2x \): \[ y = 100 + 2(10) \] \[ y = 100 + 20 \] \[ y = 120 \] Hence, the total costs to the retailer are: \[ \$[/tex]120 \]

4. Total Revenue from Selling 10 Items:

Using the revenue equation [tex]\( y = 15x \)[/tex]:
[tex]\[ y = 15(10) \][/tex]
[tex]\[ y = 150 \][/tex]

Hence, the total revenue from selling 10 items is:
[tex]\[ \$150 \][/tex]

5. Profit Calculation:

Profit is the difference between the total revenue and the total costs. Therefore:
[tex]\[ \text{Profit} = \text{Total Revenue} - \text{Total Costs} \][/tex]
[tex]\[ \text{Profit} = 150 - 120 \][/tex]
[tex]\[ \text{Profit} = 30 \][/tex]

Hence, the profit for this retailer is:
[tex]\[ \$30 \][/tex]

To summarize:

- Cost equation: [tex]\( y = 100 + 2x \)[/tex]
- Revenue equation: [tex]\( y = 15x \)[/tex]
- Total costs when 10 items are made: [tex]\( \$120 \)[/tex]
- Total revenue from selling 10 items: [tex]\( \$150 \)[/tex]
- Profit for the retailer: [tex]\( \$30 \)[/tex]
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