Part II: Sensitivity analysis (10 marks, 2 marks per subquestion) A garden store prepares various grades of pine bark for mulch: muggets (x1),mini nuggets (c), and chips (x3). The production process requires pine bark, machine time, and labour time. Each bag of nuggets requires 5 pounds of barks, 2 minutes of machine time, and 2 hours of labour time To produce one bag of mini-nuggets, 6 pounds of barks, 4 minutes of machine time, and 4 hours of labour time are needed The production of one bag of chips consumes 3 pounds of barks, 5 minutes of machine time, and 3 labour hours. The store has 600 pounds of barks, 660 minutes of machine time, and 480 hours of labour time available for the next production run. The demand for the three products is at least a total of 150 bags. The unit profit contribution of nuggets, mini-muggets, and chips are $9. $9, and $6 per bag, respectively. The following linear programming model has been developed Decision variables x1 = bags of nuggets to produce x2 = bags of mini-nuggets to produce x3 = bags of chips to produce Objective function Maximize z=9x1 + 9x2 + 6x3 Constraints: Bark: 5x + 6x2 + 3x3 0 The Excel Solver sensitivity report is given on the next page, please answer the following questions based on the report NOTE: 1. EACH QUESTION THAT FOLLOWS REFERS TO THE ORIGINAL PROBLEM. THAT IS, EACH QUESTION IS INDEPENDENT OF THE OTHER QUESTIONS. 2. IF IT IS IMPOSSIBLE TO ANSWER THE QUESTION WITHOUT USING THE COMPUTER, YOU MUST STATE THAT IN YOUR ANSWER AND BRIEFLY EXPLAIN WHY. 3. NO MARKS WILL BE GIVEN FOR UNSUPPORTED ANSWERS CALCULATIONS SHOULD BE DONE IN THE SPACE PROVIDED. CLEARLY PRINT YOUR ANSWER IN THE BOX PROVIDED. 4. ALL EXPLANATIONS MUST BE LIMITED TO 15 WORDS. ONLY THE FIRST 15 WORDS OF YOUR EXPLANATION WILL BE READ BY THE MARKER Sensitivity Report Adjustable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient increase Decrease $B$10 Bags of Nugget 53.6842 0 9 1 2.166667 $C$10 Bags of Mini-nugget 0-2.05263 9 2.0526316 1E+30 $D$10 Bags of Chip 110.526 0 6 16.5 0.6 Constraints Cell Name $B$17 Bark LHS $B$18 Machine LHS $B$19 Labour LHS $B$20 Demand LHS Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 600 1.73684 600 195 90 660 0.15789 660 86.666667 135 438.947 0 480 1E+30 41.05263 164.211 0 150 14.210526 1E+30 (1) What are the optimal solution and its objective function value? Answer = . x3 = The objective function value is: Explain where you find this information and show your calculation of the objective function value below (clearly PRINT no more than 15 words): I Calculation (2) What is the impact on the optimal solution and the objective function value if the unit profit contribution for mini-nuggets increases from $9/bag to $10/bag? Calculations Answer (Complete ONE appropriate box ONLY) Current solution remains optimal. Mark X here: The new objective function value is: Explain (clearly PRINT no more than 15 words): The problem must be re-solved on the computer. Mark X here: Explain (clearly PRINT no more than 15 words): (3) After the production process 80s on for one week, the manager found that each bag of nuggets needs only 4 pounds of Tarks rather than 5. What is the impact on the objective function value if this error is corrected? Calculations Answer (Complete ONE appropriate box ONLY) (3) After the production process goes on for one week, the manager found that each bag of nuggets needs only 4 pounds of barks rather than 5. What is the impact on the objective function value if this error is corrected? Calculations Answer (Complete ONE appropriate box ONLY) The impact on the objective function can be obtained without resolving the problem on the computer. Mark X here: The new objective function value is: Explain (clearly PRINT no more than 15 words): The problem must be re-solved on the computer. Mark Xhere: Explain (clearly PRINT no more than 15 words): I (4) If the supplier does not have enough barks and hence, provides only 550 pounds of barks to the manager, what is the impact on the objective function value? Calculations Answer (Complete ONE appropriate box ONLY) The impact on the objective function can be obtained without resolving the problem on the computer. Mark X here: The new objective function value is: Explain (clearly PRINT no more than 15 words): The problem must be re-solved on the computer. Mark X here: Explain (clearly PRINT no more than 15 words): (5) The manager has been notified that he should not worry about the availability of labour hours as another production line has been closed due to the recent economic turmoil. Therefore, there will be unlimited labour hours available in the context of the size of this particular business) to him without any additional cost. What is the impact on the optimal solution and the objective function value? Calculations I Answer (Complete ONE appropriate box ONLY) Current solution remains optimal. Mark X here: The new objective function value is: Explain (dearly PRINT no more than 15 words: The problem must be re-solved on the computer. Mark X here: Explain (clearly PRINT no more than 15 words)