Problem 3: FaceMask Production Mix The FaceMask Malaysia Sdn Bhd produces four types of masks: 3 Ply Medical Face Mask, 4 Ply Medical Face Mask, KN94, and KN99. Each item requires goes through the production process including folding, shaping and cutting the masks, welding the ear loops and sterilization before bagging. The following table shows the profit, and time required per 100 items in each process. The last column shows the total number of hours available each week. Due to the recent COVID-19 outbreak, the company has decided to produce at least 1,000 for each item. (i) Develop the Linear Programming Model for the above problem. (12 marks) Show your Answer and Sensitivity reports, without invoking the Solver answer the following questions: (ii) Find the company's most profitable production plan using Solver. How many of each type of mask should be produced to achieve a maximum profit? Calculate the maximum profit of the company. (6 marks) (iii) Suppose the profit for producing each KN99 has increased from RM154 to RM 165 , would the optimal production schedule and profit change? Explain. (4 marks) (iv) Are there any resources left over when the maximum profit is achieved? If so, list all resources left over and the quantities of each. (5 marks) (v) Management is considering to allocate ten hours of overtime in one department. How to allocate these hours? Why? What is the new maximum profit? (5 marks) (vi) State the shadow price for the weld the ear loops time. Interpret the answer. (4 marks) (vii) If the company increases extra five hours of bagging time, predict the company's maximum profit. Should the company add more bagging time? Why or why not? (4 marks)