Question

the figure shows the graph of the cost and revenue functions for a company that manufactures and sells external hard drives. the solid line represents the revenue function, r(x) = 45x; the dashed line represents the cost function, c(x) = 3000 + 33x. how many hard drives must be produced and sold for the company to break even? the company must produce and sell \square hard drives to break even.

Explanation:

Step1: Set revenue equal to cost

To break even, \( R(x) = C(x) \). So we set \( 45x = 3000 + 33x \).

Step2: Solve for x

Subtract \( 33x \) from both sides: \( 45x - 33x = 3000 + 33x - 33x \), which simplifies to \( 12x = 3000 \). Then divide both sides by 12: \( x = \frac{3000}{12} \).

Step3: Calculate the value of x

\( \frac{3000}{12} = 250 \).

Answer:

250