You are planning to buy metal sheet cutting machines for your site. Your supplier has two models: Model A can cut 200 sheets a day, but costs $6000. Model B can cut 100 sheets a day, but costs $4000. You need at least six such machines, of which at least one machine must be Model A. In total, the machines must handle at least 750 sheets a day. (a) You are told to determine the mix of the two cutting machines that will fulfil all the requirements at minimum cost. Express the decision variables and the objective function mathematically. (b) Formulate the problem as an Integer Program. [3 marks] [4 marks] (c) Using a graphical method or otherwise, determine the optimal solution to the problem. You may use the graph paper provided. In your graphical solution, show clearly the feasible solution space; label the constraints and the objective function at the optimal solution. [6 marks] (d) Your machine supplier can offer you a special package: If you buy 3 machines of the same type, he can give you a 20% discount for the 3 machines. For example, if you buy 4 machines, the price of the first 3 machines is reduced by 20%, while the price of the 4th is not changed. All other constraints remain the same. Reformulate the above problem as an Integer Program. (Hint: You need to change your decision variables to suit the new problem.) [7 marks]