Standard form

Problem 4 (20 marks in total). You are given the following linear programming problem. minO.12x+0.15y St. 60x+ 60y 300 12x + 6y 36 IOx+30y>90 x, y 20 (a) (2 marks) Write the standard form of the problem. (b) (1 mark) Is the standard form also the tableau form? Explain. (c) (3.5 marks) Graph the solution space using the first two constraints. (d) (1.5 marks) Now, graph the solution space using all three constraints. Does the solution space change by adding the last constraint? Explain. (e) (4.5 marks) Find the extreme points of the problem (with all three constraints). (f) (1.5 marks) Find an optimal solution. (g) (4 marks) What would happen to the optimal solution found in (g) if the coefficient of x in the objective function was decreased from 0.12 to O. 10? Justify your answer with appropriate calculations.