Question

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.

1) 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.

2) Graph the inequalities.

3) What is the maximum number of hours Lia can work at the restaurant and still meet her earnings goal? Explain.

4) What is the maximum amount of money

Answer 1

hi

Answer 2

Hello

Answer 3

First identify the DECISION VARIABLES.
Here, the hours worked at the restaurant and at the yard are the two decision variables.
Let x= the number of hours worked at the restaurant and
y=the number of hours worked at the yard.

Answer 4

ok

Answer 5

Next step is to setup an OBJECTIVE FUNCTION/TARGET FUNCTION.
It must be something like Maximize/minimize
Here,profit is the Objective.
Total profit Lia can get if she work for $8 per hour in restaurant and $12 per hour in yard will be:
P=8x+12y
So our objective is to,
Maximize P=8x+12y.

Answer 6

so that would be question 2 or question 1?

Answer 7

1

Answer 8

ok thank you

Answer 9

hey @Error1603 would r=15-8r and y=15-12y?