Question 2: Linear Programing Formulation (15 marks) A division of the Happy tire Company thinks of making a new set of two products "A" and "B" to be processed in three departments 1, 2 and 3. Each product will require a certain amount of processing time in each department according to the Product A Product B Availability Department 1 0.3 hour 0.7 hour 90 hours following table: Department 2 0.45 hour 0.3 hour 70 hours Department 3 13 minutes on slide 0.2 hour 0.65 hour 100 hours Max production 150 130 Each unit of products A and B contributes $54 and $73 to profit respectively. To produce product A, there is a fixed cost of $810 setting up the production line which is $610 for product B. How many of each product should be made to optimize the profit of this division? Formulate the problem (Introduce variables, objective function and constraints properly, but do not attempt to solve)