It takes $20$ hours and $\$400$ to interview a candidate, and it takes $120$ hours and $\$3,600$ to train an employee. A company has less than $\$95,000$ to interview and train employees, and it wants to spend at most $470$ hours to do so. Let $C$ denote the number of candidates they interview and $E$ the number of employees they train. Write an inequality that represents the condition based on the number of dollars the company can spend. $\newline$ Write an inequality that represents the condition based on the number of hours the company wants to spend.

Full solution

Q. It takes

20

hours and

\$400

to interview a candidate, and it takes

120

hours and

\$3,600

to train an employee. A company has less than

\$95,000

to interview and train employees, and it wants to spend at most

470

hours to do so. Let

C

denote the number of candidates they interview and

E

the number of employees they train. Write an inequality that represents the condition based on the number of dollars the company can spend.

\newline

Write an inequality that represents the condition based on the number of hours the company wants to spend.

Calculate Total Cost: Calculate the total cost for interviewing and training candidates and employees. $\newline$ Cost = $20C + 400C + 120E + 3600E$ $\newline$ Simplify the expression. $\newline$ Cost = $420C + 3720E$
Write Cost Inequality: Write the inequality for the cost constraint. $\newline$ The company has less than $\$95,000$ to spend. $\newline$ $420C + 3720E < 95,000$
Calculate Total Time: Calculate the total time spent on interviewing and training. $\newline$ Time = $20C + 120E$
Write Time Inequality: Write the inequality for the time constraint. $\newline$ The company wants to spend at most $470$ hours. $\newline$ $20C + 120E \leq 470$