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Regarding your constraint equations:
8x+7y is a production cost expression. The equation
you want is 8x+7y<=126
You also need a production time eqation:
4x + 3y <= 58
Also x>=0 and y>=0
The Objective Function is an Income statement:
Income or I = 15x + 12y
Graph the four constraint lines on a single pair of xy axes.
The lines will form a triangle with two intersections on the
y-axis and one where the production-cost and the production-
time lines intersect.
Find the three points of intersection.
Put the (x,y) values into the objective function to determine
under what production conditions you maximize your income and
therefore your maximize profit.