Question 7: Sensitivity analysis (20 marks) A garden store prepares various grades of pine bark for mulch: nuggets (xi), mini-nuggets (x2) 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- nuggets, and chips are $9, 89, and $6 per bag, respectively. The following linear programming model has been developed Decision variables x - bags of nuggets to produce x3 = bags of mini-nuggets to produce x3 = bags of chips to produce Objective function Maximize z = 9x1 + 9x2 + 6x3 Constraints: Bark: 5x + 6x2 + 3x3