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