do it manually without using software

SENSITIVITY AND POST OPTIMAL ANALYSIS (70 points) QL. The Dammam Furniture Company manufactures desks, tables, and chairs. The manufacture of cach type of furniture requires lumber and two types of skilled labor finishing and carpentry. The amount of each resource needed to make each type of furniture is given in the following table. Resource Desk Table Chair Lumber board ft) 8 Finishing hours 4 2 13 Carpentry hours 2 15 05 Currently, 48 board feet of lumber, 20 finishing hours, and 8 carpentry hours are available. A desk sells for 560, a table for $30, and a chair for $20. Because the available resources have already been purchased, Damntam wants to maximize total revenue Defining the decision variables as Xi - number of desks produced x2 number of tables produced xnumber of chairs produced Following is the initial LP formulation of the problem Maximize x = 60x4 + 30x2 + 20% Subject to 8x + 6xy + xy S 48 3 4x2 + 2xy + 2x, 5 20 1 2x + 3x + 2x 58 sy, X, 20 The optimal tableau for this problem is then (solving by Simpler Method) is BV 3. 31 5: 2 0 5 0 0 10 S: 0 0 ! 2 0 1 0 2 X; 1 5/4 0 0 -1/2 10 - -4 3/2 RHS 280 24 8 2 Now, find the optimal solution using sensitivity and post optimal analysis for the following changes to the original problem: (10 points each) 1481 (a) Available resources change to 30 (b) Prices of table changed to $33 te) Prices change to $600 per desk, 845 per table and $30 per chair. (d) Suppese due to market requirements, the total number of products made by Dummam should be at most 12. (Sum of all products is 12), how does that affect the optimal solution. (c) Considering making new footstools, the price of each footstool is $15 and requires 1 board foot of lumber. I finishing hour and I carpentry hour. What will be the optimal product mix? (1) For what change in price of table will the current solution remain optimal? (8) There is a decrease in supply for lumber, what is the range of change that will keep the current solution optimal