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.
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
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