Question

the figure shows the graphs 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) = 55x ), the dashed line represents the cost function, ( c(x) = 5400 + 37x ). 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

Set \( R(x)=C(x) \), so \( 55x = 5400+37x \).

Step2: Solve for \( x \)

Subtract \( 37x \) from both sides: \( 55x-37x=5400+37x - 37x \).
This gives \( 18x = 5400 \).
Then divide both sides by \( 18 \): \( x=\frac{5400}{18}\).
Since \( \frac{5400}{18}=300 \).

Answer:

\( 300 \)