A tire company is selling two different tread patterns of tires. Tire x sells for $75.00 and tire y sells for $85.00.Three times the number of tire y sold must be less than or equal to twice the number of x tires sold. The company has at most 300 tires to sell.
What is the maximum revenue that the company can make?
We can solve this with a graph [ linear programming ]
Let x = number of $75 tires to be sold and y = the number of $ 85 tires to be sold
Here are the constraints to be graphed :
x + y ≤ 300
3y ≤ 2x
And the objective function to be maximized is this
75x + 85y
A look at the graph here : https://www.desmos.com/calculator/5dtkxwrxak will show that the max occurs at the corner points of the intersection of the two inequalities
There is only one corner point at ( x , y) = (180, 120)
Putting this into the objective function produces
75(180) + 85 (120) = $ 23700