(a) A company makes two products, Alpha-4 and Beta-5. These two products are processed using two machines, M and M. Each unit of Alpha-4 requires 5 hours of processing time in M and 5 hours of processing time in M. Each unit of Beta-5 requires 3 hours of processing time in M and 6 hours of processing time in M. In a month, M can run for a maximum of 220 hours and M 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)