Formulate a LP model for the following situation: $$A carpenter makes Tables and Chairs. Each Table cost $$30$ to be made and can be sold for $$70.$ Each Chair cost $$16$ and can be sold for $$42.$ The carpenter can afford to spend up to $40$ hours per week working and takes five hours to make a table and two hours to make a chair. Due to a space limitation in the shop, at most $40\%$ of all the production $($Tables and Chairs$)$ has to be Tables. By experience he knows that the maximum number of chairs that he can sell in any given week is $30.$ Formulate this problem as a LP model, describe the decision variables $($think about what are those things that you can control$)$ and explain what are some of the assumptions that you made modeling the situation. Submit your analysis as an attached document.