Question: The figure on the right shows the graphs of the cost and revenue functions for a company that…

The figure on the right shows the graphs of the cost and revenue functions for a company that manufactures and sells small radios. How many radios must be produced and sold for the company to break even?

The number of radios that must be produced and sold in order to break even is \(\boxed{\text{radios}}\).

[Graph]

• \(C(x) = 22,500 + 17x\)
• \(R(x) = 47x\)

[Axes]

• \(x\)-axis: Radios Produced and Sold
• \(y\)-axis: Dollars

Solution

Let’s solve for the number of radios that must be produced and sold to break even. \[ 7x = 22500 + 17x \] Subtract \(17x\) from both sides: \[ 7x - 17x = 22500 \] \[ -10x = 22500 \] Divide both sides by \(-10\): \[ x = -2250 \] Since the number of radios produced and sold cannot be negative, there is no break-even point for positive values of \(x\).