Problem 4 (20 marks in total). You are given the following linear programming problem. min0.12x+0.15ys..60x+60y30012x+6y3610x+30y90x,y0 (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 0.10 ? Justity your answer with appropriate calculations. Problem 5 (10 marks). An operations manager is trying to determine a production plan for the next week. There are three products (say, P, Q, and Q) to produce using four machines (say, A and B, C, and D), Each of the four machines performs a unique peocess. There is one machine of each type, and each machine is available for 2,400 minutes per week. The unit processing times for each machine is given below: The unit revenues and maximum sales for the week are indicated in the following table: 4 Maximum sales 100 40 60 Storage from one week to the next is not permitted. The operating expenses associated with the plant are $6,000 per week, regardless of how many components and products are made. The $6,000 includes all expenses except for material costs. The operations management wants to find the best product mix. Help him/her formulate the problem as a mathematical program