Chapter 1.5, Problem 55PE

For Exercises 55-56, the fixed and variable costs to produce an item are given along with the price at which an item is sold. (See Example 6)

a. Write a linear cost function that represents the cost $C\left(x\right)$ to produce $x$ items.

b. Write a linear revenue function that represents the revenue $R\left(x\right)$ for selling $x$ items.

c. Write a linear profit function that represents the profit $P\left(x\right)$ for producing and selling $x$ items.

d. Determine the break-even point.

$\begin{array}{l}\text{Fixed cost: \$2275}\\ \text{Variable cost per item: \$34}\text{.50}\\ \text{Price at which the item is sold: \$80}\text{.00}\end{array}$