Hello. Solve the exercise step by step, please.

A machine can make a product A at 1,000 per hour or product B at 2,000 per hour. The available total production time is 2,400h/yr. Annual fixed cost are $80,000. Other data are: Where NA is the yearly production units of products A. Find the allocation of products which give the mximum gross profit per year, likewise show that you have actually found the solution. Use Direct Substitution , Lagrange Multipliers and Constrained Variation methods