Question

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a firm will break even (no profit and no loss) as long as revenue just equals cost. the value of x (the number of items produced and sold) where c(x)=r(x) is called the break - even point. assume that the below table can be expressed as a linear function. find (a) the cost function, (b) the revenue function, and (c) the profit function (d) find the break - even point and decide whether the product should be produced, given the restrictions on sales

fixed cost	variable cost	price of item

according to the restriction, no more than 20 units can be sold
(a) the cost function is c(x)=300 + 15x
(simplify your answer.)
(b) the revenue function is r(x)=25x
(simplify your answer.)
(c) the profit function is p(x)=□
(simplify your answer.)

Explanation:

Step1: Recall Profit Function Formula

Profit function \( P(x) \) is revenue minus cost, so \( P(x) = R(x) - C(x) \).

Step2: Substitute \( R(x) \) and \( C(x) \)

We know \( R(x) = 25x \) and \( C(x) = 300 + 15x \). Substitute into the formula:
\( P(x) = 25x - (300 + 15x) \)

Step3: Simplify the Expression

Distribute the negative sign: \( P(x) = 25x - 300 - 15x \). Combine like terms: \( P(x) = (25x - 15x) - 300 = 10x - 300 \).

Answer:

\( 10x - 300 \)