Question 3 A firm that assembles computers and computer equipment is about to start production of four types of microcomputers. Each type will require assembly time, inspection time, packaging time and storage space. The amounts of each of these resources that can be devoted to the production of the Hours/Unit Product Line A Line B X Y 12 4 4 8 Total Hours 60 40 3 microcomputers is limited. The manager of the firm would like to determine the quantity of each microcomputer to produce in order to maximize the profit generated by sales of these microcomputers. In order to develop a suitable model of the problem, the manager has met with design and production personnel. As a result of those meetings, the manager obtained an information which was then converted into a mathematical model Thus: X1 = Quantity of type 1 to produce X2 = Quantity of type 2 to produce X3 = Quantity of type 3 to produce X4 = Quantity of type 4 to produce Zmax = 0.50X1 + 0.20X2 + 0.30X3 + 0.80X4 Subject to: Assembly 200X1 + 200X2 + 150X3 + 250X4 50,000 Inspection: 3X1 + 2X2 600 Packaging: 2X1 + 2X2 + 4X3 +4X4 1,000 Storage: 2X1 + 4X2 + X3 + 5X4 800 Non-negativity: X1, X2, X3, X4 0 a) Use the excel solver on the simplex method to solve the problem (show the answer report, sensitivity report and limit report) EV(10 Marks) b) If the firm increases the per unit profit of Type 4 to GHC 0.9, what will be the effect on the optimal solution and the total profit EV (10 marks) c) The firm wants its customers to also have least a Type 3. For this Type 3 microcomputer, determine the per unit profit that would result in at least a unit of it being produced