Hi can you help with detailed solution on this problem below:

A furniture manufacturer produces two types of tables (country and contemporary) using three types of machines. The country model requires 1.5 hours on a router, 3 hours on a sander and 2.5 hours on a polisher.The contemporary table requires 2 hours on a router, 4.5 hours on a sander and 1.5 hours on a polisher. The total machine time available per week are 1000, 2000 and 1500 for the router, sander and polisher respectively.

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?

part a First solve this as an LP and derive the optimal solution and the optimal objective function value (you may include just one place after the decimal in your solution)

part b Next, solve this as an ILP and derive the optimal solution and optimal objective function value (to solve as an Integer Linear Program, you will have to add a constraint that the decision variables are "int", similar to how you indicate that decision variables are "bin" for binary.

part c Would you have been able to derive the solution to the ILP by rounding the solution to the LP