Suppose we have 15000 units of cash at hand. There are five investment possibilities. Investment 1 requires 5000 units and it has a return value of 9000 units. Investment 2 requires 6500 units and it has a return value of 10000 units. Investment 3 requires 3500 units and it has a return value of 7000 units. Investments 4 requires 3000 units and it has a return value of 4000 units. Investment 5 requires 5500 units and it has a return value of 7500 units. (a) (b) Formulate this problem as a linear programming problem with the aim to maximize the total return value. Compute the optimal solution using the Gurobi software. Show the input script and output solution of the software. Summarize the optimal solution. (8 marks) A new constraint is now imposed: If Investment 1 is made, Investment 4 must also be made too. Formulate this problem as a linear programming problem with the aim to maximize the total return value. Compute the optimal solution using the Gurobi software. Show the input script and output solution of the software. Summarize the optimal solution. (8 marks) (c) Explain the difference between the optimal z values for Question 5(a) and (b). (4 marks)