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A company makes a profit of $50 per software program and $35 per video game. The company can produce at most 200 software programs and at most 300 video games per week. Total production cannot exceed 425 items per week. How many items of each kind should be produced per week in order to maximize the profit? Use linear programming to solve

 
Guest Sep 12, 2017
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Let  x be the number of $50  software programs that should be produced

Let y be the number of $35 video games that should be produced

 

And we have these two constraints

 

x ≤ 200     and  y ≤ 300

 

Also....we have the constraint that

 

x + y   ≤  425

 

And we want to  maximize this :   50x  + 35y

 

Look at the folowing graph of these  constrraints :  https://www.desmos.com/calculator/2gpyq2qxwl

 

The  possible solutions  occur at the corner points of the intersections  of the three constraints

 

These occur at  ( x, y)   = (125 , 300)  and  (200 , 225)

 

Putting these  into       50x  +  35y

 

(125, 300)  =   50(125) + 35(300)   =  $16750

 

And

 

(200, 225)  =  50(200) + 35(225)  = $17875

 

So......producing 200 software programs and  225 video games will maximize the profit

 

 

 

 

cool cool cool

 
CPhill  Sep 12, 2017

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