3 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 SMALL RHS Equation for CHAIRS SOFA Masimi 17 25 Max LOUNGE CHAIRS 25SMALL SOFA FRAMING LABOR 3.5 500 SLOUNGE CHAIRS. SMALL pertem SOFAS CUTTING LABOR 25 300 2 SLOUNGE CHARS SMALL perem SOFA 300 Yards of Material 8.5 10.5 ESLOUNGE CHAIRS pert 30.SSMALL SOFA - 150 Machine Hours per 1.5 3 200 1.SLOUNGE CHARS SMALL SOFA 200 MIN NUMBER OF . >25 LOUNGE CHAIRS CHAIRS OPTIMAL SOLUTION LOUNGE SMALL RHS Dual CHAIRS SOFA Maxime 17 25 FRAMING LABOR 35 500 perem CUTTING LABOR 25 3 perem Yards of Material 6.5 10.5 350 perem Machine Hours per 15 3 200 3.3333 them MIN NUMBER OF . CHAIRS Solutions 100 16.6667 21166 67 150 Upper Bound 20.83 34 Bound RANGING TABLE Variable Value Reduced Original Cost Val und LOUNGE CHAIRS 100 17 SMALL SOFA . Constraint Dual SlackSurplus Original Lower Value Val Bound FRAMING LABOR pero Hem CUTTING LABOR per 45 30 228 item Yards of Material per 25 Hem Machine Hours pertem 3.83 MIN NUMBER OF . 75 CHAIRS 320 211.11 100 12. What are the optimal number of Lounge Chairs and Small Sofas to produce and what is the total profit? 105 3 C 200 2.3333 Yards of Material 65 per em Machine Hours per 1.5 MIN NUMBER OF 1 CHAIRS Solution 100 O > 25 16.6667 21166 Cost Bound 34 Upper Bound RANGING TABLE Value Reduced Original LOUNGE CHAIRS 100 SMALL SOFA 25 Constraint Dual Slack/Surplus Original Lower Val Bound FRAMING LABOR pero CUTTING LABOR per 45 300 225 item Yards of Material per 0 25 ase 25 Hem Machine Hours per Hem 3.83 . 200 MIN NUMBER OF 0 75 CHAIRS 320 21.11 100 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 comer point? RHS Equation form SMALL SOFA 25 6 500 PROBLEM STATEMENT LOUNGE CHAIRS Maximize 17 FRAMING LABOR 3.5 per item CUTTING LABOR 2.5 per item Yards of Material 6.5 per Item Machine Hours per 1.5 Item MIN NUMBER OF 1 CHAIRS 3 ca 300 Max 17LOUNGE CHAIRS 25SMALL SOFA 3.5LOUNGE CHAIRS + 6SMALL SOFA = 25 10.5 = 25 OPTIMAL SOLUTION LOUNGE CHAIRS Maximize 17 RHS Dual SMALL SOFA 25 6 100 3 = 25 0 16.6667 2116.6 67 RANGING TABLE Variable Value LOUNGE CHAIRS 100 SMALL SOFA 16.67 Constraint Dual Value FRAMING LABOR per 0 item CUTTING LABOR per 4.5 item Yards of Material per 0 Item Machine Hours per Item 3.83 MIN NUMBER OF 0 CHAIRS Reduced Original Cost Val 17 25 Slack/Surplus Original Val 50 500 oo Lower Bound 12.5 20.4 Lower Bound 450 Upper Bound 20.83 34 Upper Bound Infinity 0 300 225 320 25 850 825 Infinity 0 200 180 211.11 100 75 25 0