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