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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?

\$13,500

\$22,500

\$23,700

\$25,500

Sep 19, 2017

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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

Sep 19, 2017