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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

Guest Sep 19, 2017
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 #1
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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

 

 

cool cool cool

CPhill  Sep 19, 2017

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