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# Help..

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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. Show all your work.

Sep 27, 2018

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Let x be the number of  software programs to be produced and y  be the number of  video games to be produced

We have this system of constraints

x ≤ 200

y≤ 300

x + y ≤ 425

And we wish to maximize this objective function

50x  + 35y

Look at the graph of the constraints, here : https://www.desmos.com/calculator/bbbhypnku7

The possible values  of (x , y)  occur at the corner points of the feasible  region , namely at (125, 300)  or ( 200, 225)

Plugging these into the objective function, we get

50(125) + 35(300)  =   \$16,750

50(200) + 35(225)  =  \$17,875

Then....200 software programs should be produced and  225 video games should be produced

Sep 27, 2018
edited by CPhill  Sep 27, 2018
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