Question

practice exercises lesson 7.3b
possible points: 10
a company manufactures and sells radios. it costs them $10,000 to start the company and $30 to make each radio. they sell each radio for $50. write and equation for the cost of manufacturing the radios (c) and an equation for the revenue (profit) made from selling the radios (r). let x represent the amount of radios produced and sold.
use your equation from the previous problem to find out how many radios they have to sell to break even.
○ 700 radios
○ 500 radios
○ 300 radios
○ 100 radios

Explanation:

Step1: Define Cost and Revenue

Cost function \( C(x) = 10000 + 30x \) (fixed cost + variable cost per radio).
Revenue function \( R(x) = 50x \) (selling price per radio times quantity).

Step2: Break - Even Condition

At break - even, \( C(x)=R(x) \).
Set \( 10000 + 30x=50x \).

Step3: Solve for x

Subtract \( 30x \) from both sides: \( 10000 = 50x - 30x \).
Simplify: \( 10000 = 20x \).
Divide both sides by 20: \( x=\frac{10000}{20}=500 \).

Answer:

500 radios (corresponding to the option "500 radios")