Answer:
(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:
- (5,10)
- (5, 6.7)
- (15,0)
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
- At (5,10), Earning=(5X8)+(10X12)=40+120=$160
- At (5, 6.7), Earning=(5X8)+(6.7X12)=40+80.4=$120.4
- At (15,0) Earning=(15X8)+(0X12)=$120
Since she has to work at least 5 hours at the restaurant, the maximum amount possible is $160.
