Consider the following linear programming problem for questions 12-17 (15 points each) A company produces Lounge Chairs and Small Sofas. It uses Two Labor Types (Framing and Cutting time per item in hours), Material and a Machine in the manufacturing process Management has put a minimum on the number (25) of Lounge Chairs which must be produced. The profit per Lounge Chair is $17.00 and per Small Sofa is $25.00. Below are the LP formulation and the QM results tables. PROBLEM STATEMENT LOUNGE CHAIRS Maximize 17 RHS Equation form SMALL SOFA 25 6 = 25 Yards of Material 6.5 10.5 25 MIN NUMBER OF CHAIRS RHS Dual OPTIMAL SOLUTION LOUNGE CHAIRS Maximize 17 SMALL SOFA 25 CO 25 1 0 0 MIN NUMBER OF CHAIRS Solution-> 100 16.6667 2116 .667 RANGING TABLE Variable Value Lower Bound 12.5 Upper Bound 20.83 LOUNGE CHAIRS 100 20.4 Reduced Original Cost Val 0 17 0 25 Slack/Surpl Original us Val 50 500 SMALL SOFA Constraint 34 16.67 Dual Value 0 Lower Bound 450 Upper Bound Infinity 4.5 0 300 225 320 0 25 850 825 FRAMING LABOR per item CUTTING LABOR per item Yards of Material per Item Machine Hours per Item MIN NUMBER OF CHAIRS Infinity 3.83 0 200 180 211.11 0 75 25 0 100 12. What are the optimal number of Lounge Chairs and Small Sofas to produce and what is the total profit? 13. Which constraints are active, meaning that all of the resource is used in the optimal solution? 14. For the Cutting Labor per item constraint, how much additional profit can be made by adding 10 hours of Cutting Labor per item resource available? 15. What is the amount of increase in profit for each Machine Hour added and what is the maximum number of yards that can be added for this amount of profit increase? 16. How much profit is added if you are given an additional 50 Yards of Material? 17. By how much can I increase the profit per Small Sofa before the solution shifts to another corner point