give step by step solution and show working

PROBLEM 3. (10 POINTS) Uncle Ulysses operates a small business: he produces three types of houses to sell to people wanting to get back to nature. Based on your discussion with your uncle you construct the following table based on your understanding of his weekly availability of labor. Item Profit/Unit Fabrication Assembly Painting Crating Birdhouse S9 1 2.5 0.25 Doghouse Outhouse 1.75 2 0.75 Capacity 30 hours 50 hours 20 hours 20 hours 1 S8 1.25 1.5 0.5 0.5 SS 4 Based on the information in the table, you formulate the problem as a linear program. The labor needed for fabrication, assembly, painting, and crating is all dedicated solely to each function, i.e., none of the workers have been cross-trained. Solve using the simplex algorithm