Answer Happy

a Problem decsription. You own a furniture company that produces two kinds of furniture: tables and chairs. It produces these two types of furniture from two types of parts: big parts and small parts. In order to manufacture a table one big part and two small parts are used. To manufacture a chair one small part and one big part are used. A table sells for $400 and a chair for $300. Assume that the furniture company has stocked 200 big parts and 300 small parts. The question is: How many tables and chairs should your company produce so as to maximize its profit? If the company produces Xı number of tables and x2 number of chairs, then the corresponding profit is 400x1 + 300x2. But there are constraints on Xı and 22. In order to make x1 tables, we need X1 big parts and 2x1 small parts, while to make x2 chairs, we need x2 big parts and 22 small parts. Given the number of big parts and small parts you have in your inventory this leads to two inequality constraints. Also the number of chairs and tables cannot be negative. Tasks: 1. 1 point Describe the feasible set for this problem as a set of inequality constraints. 2. 2 points Formulate the problem as a linear program in the standard form. 3. 3 points Using the standard form from the previous point find all basic solutions and select those which are basic feasible solutions. 4. 2 points In the plane X1-X2 sketch the feasible set. Carefully mark the extreme points and assign the correct coordinates to them. Then mark which points in X1-22 correspond to projections of the basic solutions that you have found in the previous point. 5. 2 points Which of the basic feasible solutions is the maximizer and what is the optimal profit ?