Chapter 6.6, Problem 26PPE

To determine

To determine a graph showing how many hours per week can be worked at each job.

Explanation of Solution

Given:

 Job mowing lawns that pays $12 per hour

Job at a clothing store that pays $10 per hour

Need to earn at least $350 per week

Can work no more than 35 hours per week

Must work a minimum of 10 h per week at the clothing store

Calculation:

Let’s consider $m=$ hours of mowing the lawn, $c=$ hours at clothing store.

 Job mowing lawns that pays $12 per hour,

Job at a clothing store that pays $10 per hour.

Need to earn at least $350 per week.

So, total earning is represented as

  $\Rightarrow 12m+10c\le 350$

Total hours of work are no more than 35 hours per week.

  $\Rightarrow m+c\le 35$

Job at a clothing store must be a minimum of 10 h per week.

  $\Rightarrow c\ge 10$

Graph:

  

The acceptable hours is represented by the small light blue triangle in the first quadrant.

Interpretation:

Therefore, graph showing how many hours per week can be worked at each job.