can help mine find the answer subject BMS

Answer ALL questions and show all the working steps. Question 1 (a) A company makes two products, Alpha-4 and Beta-5. These two products are processed using two machines, M1 and M2. Each unit of Alpha-4 requires 5 hours of processing time in M1 and 5 hours of processing time in M2. Each unit of Beta-5 requires 3 hours of processing time in M1 and 6 hours of processing time in M2. In a month, M1 can run for a maximum of 220 hours and M2 can run for a maximum of 180 hours. The production cost for Alpha-4 and Beta-5 are $100 and $120 per unit, respectively. Each unit of Alpha-4 and Beta-5 are sold to the vendor at $150 and $160, respectively. The company wishes to produce at least 20 units of Alpha-4 and not more than 40 units of Beta-5. The manager wishes to maximize the profit per month, within the given constraints. Formulate a linear programming model for the above problem. (12 marks) (b) Given the following linear programming formulation, obtain the optimal solution using the graphical method. (13 marks)