Q2. (30 marks) Consider the following problem: Maximize Z = X1 + 3X2 Minimize Z2 = 4X1 + X2 Subject to 5X1 +2X2 10 X1 > 0, X2 > 0 a. Solve the problem separately for goal Z and Z2 (15 marks) b. Using Global Criterion methods, formulate the model when p = 1 and p = 2 (10 marks) c. Define compromise solution set with p = 1 (5 marks) Q3. (30 marks) Consider the following problem: Maximize 2 = 2X1 + 2X2 + 3X3 Maximize Z2 = 1.5X1 + 3X2 + 2X2 Maximize Zz = X1 + 1.5X2 + 2X3 Subject to 3X1 + 2X2 + 2X35 24 (1) X1 + X2 + 2X3 0 Given unit price of resource (1) is $1, resource (2) is $1.2 and budget B = $55 a. Identify the minimum budget B*and its corresponding resource allocation. (15 marks) b. Use the optimum - path ration (r) to obtain the final solution. (10 marks) c. Given budget B1= $ 57, let find corresponding resource allocation (b1, b2, z1, 22, 23). (5 marks) Q2. (30 marks) Consider the following problem: Maximize Z = X1 + 3X2 Minimize Z2 = 4X1 + X2 Subject to 5X1 +2X2 10 X1 > 0, X2 > 0 a. Solve the problem separately for goal Z and Z2 (15 marks) b. Using Global Criterion methods, formulate the model when p = 1 and p = 2 (10 marks) c. Define compromise solution set with p = 1 (5 marks) Q3. (30 marks) Consider the following problem: Maximize 2 = 2X1 + 2X2 + 3X3 Maximize Z2 = 1.5X1 + 3X2 + 2X2 Maximize Zz = X1 + 1.5X2 + 2X3 Subject to 3X1 + 2X2 + 2X35 24 (1) X1 + X2 + 2X3 0 Given unit price of resource (1) is $1, resource (2) is $1.2 and budget B = $55 a. Identify the minimum budget B*and its corresponding resource allocation. (15 marks) b. Use the optimum - path ration (r) to obtain the final solution. (10 marks) c. Given budget B1= $ 57, let find corresponding resource allocation (b1, b2, z1, 22, 23)