Question

The revenue R for selling x fleece jackets is given by the equation R=49.75x. The cost C to produce x jackets is C=2000+17.50x. Find the number of jackets that the company needs to sell to produce a profit. (Hint: A profit occurs when revenue exceeds cost.)

Answer 1

To determine the number of jackets to sell for a profit, subtract the variable cost from the revenue equation and solve for x, resulting in the company needing to sell more than 62 jackets.

Step-by-step explanation:

To find the number of fleece jackets that the company needs to sell to make a profit, we must set the revenue function higher than the cost function. The revenue, R, is given by the equation R = 49.75x, and the cost, C, is C = 2000 + 17.50x. To achieve profit, we need R > C. By substituting the given equations, we get 49.75x > 2000 + 17.50x.

Solving the inequality step by step:

Subtract 17.50x from both sides to get 32.25x > 2000.

Divide both sides by 32.25 to solve for x, which yields x > 62. Therefore, the company needs to sell more than 62 jackets to make a profit.