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# Algebra

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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

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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   Nov 15, 2019
edited by CPhill  Nov 15, 2019