Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour. She also does yard work for $12 per hour. Lia’s parents allow her to work a maximum of 15 hours per week overall. Lia’s goal is to earn at least $120 per week. Write a system of inequalities to represent this situation. Let r be the number of hours worked at the restaurant, and let y be the number of hours of yard work. Graph the inequalities. What is the maximum number of hours Lia can work at the restaurant and still meet her earnings goal? Explain. What is the maximum amount of money Lia can earn in 1 week? Explain.

(a)

(c)Maximum number of hours Lia can work at the restaurant and still meet her earnings goal = 15 hours

(d)Maximum Earning = $160

Step-by-step explanation:

Let r be the number of hours worked at the restaurant.

Let y be the number of hours of yard work,

Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour.

Since she does yard work,

Lia’s parents allow her to work a maximum of 15 hours per week overall.

Lia’s goal is to earn at least $120 per week.

The restaurant, r pays $8 per hour

Yard work, y pays $12 per hour.

Therefore:

The system of inequalities that represent this problem is therefore:

(b)The graph of the inequality is attached below

(c)When the graph is plotted, the vertices of the feasible region are:

Where the first term is for the number of hours worked in the restaurant.

The maximum value of r possible is 15 from the three points.

Therefore, she can work at the restaurant for 15 hours and still meet her earning goal.

(d)Maximum Amount Lia can earn in 1 Week

Since she has to work at least 5 hours at the restaurant, the maximum amount possible is $160.