Question

What is the maximum revenue that the company can make?

Answer 1

23700$

Explanation:

Putting the problem in inequality, three times the number of y tires sold is less than or equal to twice the number of x tires sold:
`rarr 3y<= 2x`

Since y is more expensive and we need the maximum revenue, so we have to maximize the number of y tires sold. First let us isolate y in the inequality, by dividing both sides of the inequality by 3:
`(cancel(3)y)/cancel3<= 2/3x`
`y<= 2/3 x`

the number of y tires sold is less than or equal to two thirds of the number of x tires sold, so the maximum number that can be sold is equal to `2/3x`:
`y=2/3x`

In the given, the total number of tires sold is 300, so:
`x+y=300`

Substituting y by `2/3x`:
`x+2/3x=300`
`=5/3x=300`

Multiplying both sides of the equation by `3/5` to isolate x on the right side:
`cancel(5)/cancel3 x*cancel3/cancel5=300*3/5`
`rarr color(blue)(x=180`

Substituting value of x to find y:
`y=2/3x`
`y=2/3 *180=120`
`color(blue)(y=120`

`"total revenue"="number of units sold"*"price"`
`=x*75+y*85`
`=180*75+120*85`
`=color(red)(23700`