Question

the figure shows the graphs of the cost and revenue functions of a company that manufactures and sells small radios. use the formulas below to find ( r(100)-c(100) ). describe what it means for the company.
( r(x)=48x )
( c(x)=12,000 + 28x )
what is the value of ( r(100)-c(100) )?
( r(100)-c(100)=$ )

Explanation:

Step1: Calculate \( R(100) \)

Substitute \( x = 100 \) into \( R(x)=48x \).
\( R(100)=48\times100 = 4800 \)

Step2: Calculate \( C(100) \)

Substitute \( x = 100 \) into \( C(x)=12000 + 28x \).
\( C(100)=12000+28\times100=12000 + 2800=14800 \)

Step3: Calculate \( R(100)-C(100) \)

\( R(100)-C(100)=4800 - 14800=-10000 \)

Answer:

\( R(100)-C(100)=-\$10000 \). This means that when the company produces and sells 100 radios, the company has a loss of \( \$10000 \) (since revenue minus cost is negative, cost is greater than revenue).