A wooden furniture company can produce two different types of furniture: sideboards and chairs. Two machines are used in the production: a jigsaw and a lathe. The manufacture of a sideboard requires 3 hours on the jigsaw and 5 hours on the lathe. The manufacture of a chair requires 4 hours on the jigsaw and 2 hours on the lathe. The jigsaw can only operate 50 hours per week and the lathe can only operate W hours per week. The profit made on a sideboard is 40 dollars, and the profit made on a chair is P dollars. The values of W and P are given as follows: W = 60+ the last digit of your student number, P = 20+the second last digit of your student number. For example, if your student number is 12450267, then W=67 and P=26. The objective is to determine how many sideboards and chairs to produce each week so as to maximise the profits. (1) Formulate the problem as a linear programming problem. Ignoring the requirements that the number of sideboards and the number of chairs have to be integer. (2) Solve this linear programming problem graphically. (3) Perform the first step of solving the linear programming problem using Simplex method. (i) Transfer the problem into the Standard Format by introducing slack variables; (ii) In the graph you drew, point out which points are Basic solutions and which points are Basic feasible solutions. How many Basic solutions and how many Basic feasible solutions are there? Active Go to S (4) Use MATLAB linprog or Excel solver to solve the problem.