2. Every day after attending lectures, travel time to school and back home, sleep and rest time, on average, you should have ....... hours left to study on your coursework. (Fill the blank personally, but the number should be at least 4). You basically have two types of material to work on; quantitative and qualitative. Thus, you should plan how many hours to work on each of qualitative and quantitative material given your total available study time stated above. For every hour that you spend on qualitative material, you can increase your school performance by 15 points, while the contribution of one hour study on quantitative part is 20 points. As you should have a balanced knowledge on quantitative and qualitative skills as a management department graduate, the difference between the hours spent on quantitative and qualitative material cannot exceed 2 hours in a day. You start thinking on how to make this study plan and realize that management science can help you in decision making. So, i. Formulate your study problem as an LP model; define decision variables, objective, and constraints. ii. Draw all constraints on a graph and indicate clearly the feasible region. iii. Find graphically the optimal corner point. Infer analytically the coordinates of this optimal solution. iv. Report the optimal value of the objective function, which is your total performance point. 1. Consider the following Linear Programming problem: MinZ=3X+Y Subject to 3X284Y (C1) 5X+4Y20 (C2) 2Y16(C3) X0,Y0 i) Draw all constraints and indicate clearly the feasible region. ii) Draw the level curve for objective Z=12. iii) Find graphically the optimal solution(s). Infer analytically the coordinates of this optimal solution. iv) Report the optimal value of the objective function. v) What would be the optimal solution if objective function were changed to: a. MaxX+Y b. MinXY c. Min10X+8Y 2. Every day after attending lectures, travel time to school and back home, sleep and rest time, on average, you should have ....... hours left to study on your coursework. (Fill the blank personally, but the number should be at least 4). You basically have two types of material to work on; quantitative and qualitative. Thus, you should plan how many hours to work on each of qualitative and quantitative material given your total available study time stated above. For every hour that you spend on qualitative material, you can increase your school performance by 15 points, while the contribution of one hour study on quantitative part is 20 points. As you should have a balanced knowledge on quantitative and qualitative skills as a management department graduate, the difference between the hours spent on quantitative and qualitative material cannot exceed 2 hours in a day. You start thinking on how to make this study plan and realize that management science can help you in decision making. So, i. Formulate your study problem as an LP model; define decision variables, objective, and constraints. ii. Draw all constraints on a graph and indicate clearly the feasible region. iii. Find graphically the optimal corner point. Infer analytically the coordinates of this optimal solution. iv. Report the optimal value of the objective function, which is your total performance point. 1. Consider the following Linear Programming problem: MinZ=3X+Y Subject to 3X284Y (C1) 5X+4Y20 (C2) 2Y16(C3) X0,Y0 i) Draw all constraints and indicate clearly the feasible region. ii) Draw the level curve for objective Z=12. iii) Find graphically the optimal solution(s). Infer analytically the coordinates of this optimal solution. iv) Report the optimal value of the objective function. v) What would be the optimal solution if objective function were changed to: a. MaxX+Y b. MinXY c. Min10X+8Y