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.

oscar.a1551
Sep 27, 2018

#1**+3 **

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

CPhill
Sep 27, 2018