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1.     A company makes a profit of $10 per software program and $13 per video game. The company can produce at most 40 software programs and at most 50 video games per week. Total production cannot exceed 70 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. Show all your work.

 Nov 15, 2019
 #1
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Call x  the number of software programs and y the number of  video games 

 

Here are the inequalities that we need

 

x + y    ≤  70

x  ≤ 40

y  ≤ 50

 

And  the objective function that we wish to  maximize is

 

10x  +  13y

 

Look at the graph here :  https://www.desmos.com/calculator/xirhxowzj9

 

The corner points of the feasible region represent the possible  maximizing values

 

These  are   (20,50)   and ( 40,30)

 

Evaluating each in the objective function we have

 

10(20)  + 13(50)    =  $ 850

10(40)  +  13(30)  =  $  790

 

So.....the profit is maximized  when   40 computer programs  and  30 video games are produced

 

 

cool cool cool

 Nov 15, 2019
edited by CPhill  Nov 15, 2019
 #2
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+1

Thanks man

Guest Nov 15, 2019

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