MiMi Sdn.Bhd. produces four types of robot vacuum, each on a separate assembly line. The respective capacities of the lines are 120,100,200 and 150 vacuums per week. Type A vacuum uses 4 units of a certain electronic component, type B vacuum uses 5 units, type C vacuum uses 6 units and type D vacuum uses 2 units. The supplier of the electronic component can provide 1000 units a week. Type A vacuum uses 6 units of a certain plastic component, type B vacuum uses 11 units, type C vacuum uses 8 units and type D vacuum uses 5 units. The supplier of the plastic component can provide 2500 units a week. The prices per vacuum for the respective vacuums are RM 900, RM 800, RM 500 and RM 600. a. Formulate a linear programming model for this problem to determine the optimum daily production mix. [4 marks] b. Use a software package to solve for an optimal solution. Attach the solver output in your answer script and from the output obtained, state: i) the optimal solutions, ii) the dual prices, iii) the feasibility ranges, iv) the optimality ranges. [8 marks] c. The present production schedule (optimal solution) meets MiMi's needs. However, because of the market competition, MiMi may need to lower the price of type A vacuum. What is the lowest price that can be implemented without changing the present production schedule? [1 mark]