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

#1**+1 **

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

CPhill
Sep 12, 2017