Question

Some students want to start a business that cleans and polishes cars. It takes 1.5 hours of labor and costs $2.25 in supplies to clean a car. It takes 2 hours of labor and costs $1.50 in supplies to polish a car. The students can work a total of 120 hours in one week. They also decide that they want to spend no more than $135 per week on supplies. The students expect to make a profit of $7.75 for each car that they clean and a profit of $8.50 for each car that they polish. What is the maximum profits the students can make

Answer 1

Answer:

Answer is explained in the explanation section below.

Explanation:

Solution:

Let the variable x denotes the labor time to clean and polish the car.

Let the variable y denotes the costs to clean and polish the car.

So,

Constraints Are:

1.5x + 2y $\leq$ 120

2.25x + 1.50y $\leq$ 135

Hence,

The objective function becomes:

Function for the maximum profits students can make is

Max Z = $7.75x + $8.50y