Problem 1 Consider the following problem. Max Z = 4x + 3x2 -X1 + 6x218 -2x1 + 52 10 X1, X2 0 (con1) (con2) (a) Solve the problem if x and x2 have to be integer using graphical method. What is the optimal value of X1, X2 and Z? (10 marks) (b) Solve the problem if only x has to be integer using graphical method. What is the optimal value of x1, X2 and Z? (5 marks) Problem 3 A license to shoot a moose costs $100 for residents and $800 for non-residents. The government must decide how many licenses to issue in both categories. Demand for resident licenses appears to be unlimited; indeed, they would often have to hold a lottery to decide who received one. Demand for non- resident licenses is about 10,000 per year. At least 75% of all licenses must go to residents. The government will not issue more than 35,000 moose licenses per year. (a) Determine the optimal number of each type of license to issue if the government wants to maximize revenue. Solve the model with LINGO. How many of each type of licenses should the government issue and what is the revenue? (6 marks) (b) Suppose that the government wants annual revenues from the sale of moose licenses to be at least $10,000,100. The goal priorities in descending order of importance are (i) earn at least $10,000,100 in revenue (ii) issue at least 75% of licenses to residents, and (iii) limit the licenses to 35,000. Formulate a preemptive goal programming model for the problem. Solve the problem using LINGO. How many of each type of licenses should the government issue? Is the government able to have all its priorities satisfied? If not, which one did not get satisfied and by how much? (8 + 7 = 15 marks) (c) Solve the problem in part (b) using graphical method. Provide the optimal values for all variables, including the deviational variables. (10 marks)