Question

Equation: The total cost, in dollars, to produce x bins of cat food is given by C=16x + 6120. The revenue, in dollars, is R= −2x^2+258x. Find the profit. (Recall that profit is revenue minus cost.) At what quantity is the smallest break-even point? In other words, how many bins of cat food, x, must be produced and sold to make the profit equal to zero?

Answer 1

Profit is calculated by subtracting the cost from the revenue, resulting in a profit function P(x) = (-2x^2 + 258x) - (16x + 6120). The smallest break-even point occurs where profit equals zero, found by solving the resulting quadratic equation.

Step-by-step explanation:

To calculate the profit for producing and selling x bins of cat food, we subtract the cost from the revenue, which gives us the profit equation: P(x) = R(x) - C(x). Thus, the profit equation is P(x) = (-2x^2 + 258x) - (16x + 6120). To find the smallest break-even point, where profit equals zero, we solve the equation P(x) = 0. This entails solving the quadratic equation -2x^2 + 242x - 6120 = 0 for x. The break-even points occur where the revenue and cost functions intersect.