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

The maximum profits the students can make from cleaning and polishing cars is $1,130.

Step-by-step explanation:

To calculate the maximum profits the students can make, we need to determine the number of cars they can clean and polish within their available labor hours and budget for supplies. Let's start with cleaning cars:

Since it takes 1.5 hours of labor to clean a car and they have a total of 120 labor hours, they can clean a maximum of 80 cars (120 labor hours / 1.5 hours per car).

With a profit of $7.75 per cleaned car, their maximum profit from cleaning cars would be $620 (80 cars cleaned x $7.75 per car).

Next, let's calculate the number of cars they can polish:

Since it takes 2 hours of labor to polish a car and they have a total of 120 labor hours, they can polish a maximum of 60 cars (120 labor hours / 2 hours per car).

With a profit of $8.50 per polished car, their maximum profit from polishing cars would be $510 (60 cars polished x $8.50 per car).

To find the maximum profits, we add the profits from cleaning and polishing cars:

$620 (profits from cleaning) + $510 (profits from polishing) = $1,130

Answer 2

Answer is explained in the explanation section below.

Step-by-step 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