4.1 Form the matrix A, using the coefficients and constants in the problem constraints and objective function. 4.2 Find AT 4.3 State the dual problem. 4.4 Use the simplex method to solve the dual problem. 4.5 Read the solution of the minimization problem from the bottom row of the final simplex tableau. 5. Use the big M method to solve problem: Maximize: P = 6x1 + 2x2 subject to: x1 + 2x2 20 2x1 + x2 16 x1 + x2 9 x1 0, x2 0 6. A company manufactures outdoor furniture consisting of regular chairs, rocking chairs, and chaise lounges. Each piece of furniture passes through three different production departments: fabrication, assembly, and finishing. Each regular chair takes 1 hour to fabricate, 2 hours to assemble, and 3 hours to finish. Each rocking chair takes 2 hours to fabricate, 2 hours to assemble, and 3 hours to finish. Each chaise lounge takes 3 hours to fabricate, 4 hours to assemble, and 2 hours to finish. There are 2,500 labor-hours available in the fabrication department, 3,000 labor-hours available in the assembly department, and 3,500 labor-hours available in the finishing department. The company makes a profit of $17 on each regular chair, $24 on each rocking chair, and $31 on each chaise lounge. How many chairs of each type should the company produce in order to maximize profit? What is the maximum profit? Note: Use the simplex method.