Chapter 1, Problem 29CR

To determine

To Find: The total cost $C$ and profit $P$ for the products produced by hand tool manufacturer as a function of $x$ which is unit produced.

Answer to Problem 29CR

  $C=\text{17,500+}5.25x$ and $P=3.18x-\text{17,500}$ .

Explanation of Solution

Given Variable cost is $\$5.25$ and fixed costs are $\$17,500$ .

Selling price of the product is $\$8.43$ .

Calculation:

Expression for total cost is written as.

  $\begin{array}{l}C=\text{Fixed Cost+ Total Variable cost}\\ \text{C=17,500+ Number of units produced}\times \text{Variable cost of one unit}\\ \text{C=17,500+}x\times 5.25\\ C=\text{17,500+}5.25x\end{array}$

Therefore, expression for total is $C=\text{17,500+}5.25x$ .

Expression for profit is written as.

  $\begin{array}{l}P=\text{ Selling Price - Total Cost}\\ P=\text{Selling}\text{Price}\text{of}\text{one}\text{unit}\text{×Number}\text{of}\text{unit}-\text{Total Cost}\\ P=8.43x-\left(\text{17,500+}5.25x\right)\\ P=3.18x-\text{17,500}\end{array}$

Expression for profit is $P=3.18x-\text{17,500}$ .

So, the answer is $C=\text{17,500+}5.25x$ and $P=3.18x-\text{17,500}$ .