Country tables sell for $$350$ and contemporary tables sell for $$450.$ Management has determined that at least $20\%$ of the tables made should be country and at least $30\%$ should be contemporary. How many of each type of table should the company produce if it wants to maximize its revenue?

a$.$Formulate an LP model for this problem.

b$.$Create a spreadsheet model for this problem and solve it using Solver.

c$.$What is the optimal solution?

d$.$How will your spreadsheet model differ if there are $25$ types of tables and $15$ machine processes involved in manufacturing them?