What is the maximum revenue that the company can make?

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1 Answer
Sep 14, 2017

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#