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.
+128475 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
