Cost, Revenue \& Profit For these problems, $$ x $$ will represent the number of items and $$ y $$ will represent the money. The fixed costs for a certain item are $$ \$ 130 $$ per week. The cost to produce each item is $$ \$ 8 $$ per item. Using this information, what is the cost equation? Give your answer in slope-intercept form: The retailer intends to sell each item for $$ \$ 12 / $$ item. Using this information, what is the revenue equation? Give your answer in slope-intercept form: If in this week 36 items are made, and all items are sold in the week, what are the total costs to the retailer? Cost $$ =\$ 418 $$ What is the revenue from selling 36 items? Revenue $$ =\$ $$ Finally, what is the profit for this retailer? Profit $$ =\$ 14 $$

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**Step 1. Cost Equation**

The fixed cost is $$\$130$$ per week. The cost to produce each item is $$\$8$$ per item. This gives the cost equation in slope-intercept form:

$$
y = 8x + 130
$$

**Step 2. Revenue Equation**

Each item is sold for $$\$12$$. Thus, the revenue equation in slope-intercept form is:

$$
y = 12x
$$

**Step 3. Total Costs for 36 Items**

Substitute $$ x = 36 $$ into the cost equation:

$$
\text{Cost} = 8(36) + 130 = 288 + 130 = 418
$$

So, the total cost is $$\$418$$.

**Step 4. Revenue from Selling 36 Items**

Substitute $$ x = 36 $$ into the revenue equation:

$$
\text{Revenue} = 12(36) = 432
$$

Thus, the revenue is $$\$432$$.

**Step 5. Profit Calculation**

Profit is the difference between revenue and cost:

$$
\text{Profit} = 432 - 418 = 14
$$

So, the profit is $$\$14$$.
**Cost Equation:** $$ y = 8x + 130 $$ **Revenue Equation:** $$ y = 12x $$ **Total Costs for 36 Items:** \$418 **Revenue from Selling 36 Items:** \$432 **Profit for the Retailer:** \$14

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