Question 1) Zeki is taking 2 courses this semester: Math, and History. The GPA (Grade Point Average) is calculated as a weighted average of the course grades, where weights are the creditsMath: 4 credits, History: 2 credits. The highest possible score is 100, and the lowest possible score is 0. His course grades are linear functions of the time he spends on studying for the course, where 0 hours of preparation results in 0 marks from each course. In order to get 100 marks in Math, he needs to study 50 hours. In order to get 100 marks in History, he needs to study 40 hours. As he likes History more than Math, the number of hours he studies History should be at least as big as the number of hours he studies Math. He is willing to spend a total of 60 hours for his preparation. 1a) Formulate a linear programming model that can be used to maximize Zekis GPA. [20 marks] 1b) Solve the primal LP graphically. If it is not practical to do so, state a reason. Hint: Think about the number of axes involved. [10 marks] 1c) Write down GAMS code for solving this linear programming model. Take a screenshot of the code screen (i.e. the file with extension .gms). You need to attach this screenshot to your submission email. If you include a proper screenshot, you do NOT have to handwrite the GAMS code on your answer sheet. [10 marks] 1d) What is the maximum GPA that he can attain with the given information? If it is not possible to find the maximum value, state a reason. Please solve it on GAMS, and take a screenshot of the results screen (i.e. the file with extension .lst) making sure that the following is visible on the GAMS screen: USER: GAMS Demo license for YourName YourSurname Toros University, Turkey. You need to attach this screenshot to your submission email. Even if you include the screenshot for this question, you must still handwrite a value or explanation sentence for this question. [10 Marks] Question 1) Zeki is taking 2 courses this semester: Math, and History. The GPA (Grade Point Average) is calculated as a weighted average of the course grades, where weights are the creditsMath: 4 credits, History: 2 credits. The highest possible score is 100, and the lowest possible score is 0. His course grades are linear functions of the time he spends on studying for the course, where 0 hours of preparation results in 0 marks from each course. In order to get 100 marks in Math, he needs to study 50 hours. In order to get 100 marks in History, he needs to study 40 hours. As he likes History more than Math, the number of hours he studies History should be at least as big as the number of hours he studies Math. He is willing to spend a total of 60 hours for his preparation. 1a) Formulate a linear programming model that can be used to maximize Zekis GPA. [20 marks] 1b) Solve the primal LP graphically. If it is not practical to do so, state a reason. Hint: Think about the number of axes involved. [10 marks] 1c) Write down GAMS code for solving this linear programming model. Take a screenshot of the code screen (i.e. the file with extension .gms). You need to attach this screenshot to your submission email. If you include a proper screenshot, you do NOT have to handwrite the GAMS code on your answer sheet. [10 marks] 1d) What is the maximum GPA that he can attain with the given information? If it is not possible to find the maximum value, state a reason. Please solve it on GAMS, and take a screenshot of the results screen (i.e. the file with extension .lst) making sure that the following is visible on the GAMS screen: USER: GAMS Demo license for YourName YourSurname Toros University, Turkey. You need to attach this screenshot to your submission email. Even if you include the screenshot for this question, you must still handwrite a value or explanation sentence for this question. [10 Marks]