Question: (c) Use graphical sensitivity analysis to show that if the profit of each kilogram of Deluxe coffee is between $0.4 and $0.6, the current basis

(c) Use graphical sensitivity analysis to show that if the profit of each kilogram of Deluxe coffee is between $0.4 and $0.6, the current basis remains optimal: (i) State the slope of each binding constraint in increasing order? m1= m2= (ii) What is the current slope of the objective function? mz= (d) What would be the new optimal solution if the profit of each kilogram of Deluxe coffee is $0.65? (0) What is the new value of the objective function? z=$ (ii) What are the values of the decision variables? x1 = (e) What is the shadow price for Colombian coffee? Please answer all parts of the question. Next 120 marks] Problem 1. A coffee packer blends Brazilian coffee, Colombian coffee and Kenyan coffee to prepare two products: Super and Deluxe brands. Each kilogram of Super coffee contains 1/3 kg of Brazilian coffee, 1/3 kg of Colombian coffee and 1/3 kg of Kenyan coffee, whereas each kilogram of Deluxe coffee contains 1/6 kg of Brazilian coffee, 1/3 kg of Colombian coffee and 1/3 kg of Kenyan coffee. The packer has 6 kg of Brazilian coffee, 7 kg of Colombian coffee and 9 kg of Kenyan coffee on hand. If the profit of each kilogram of Super coffee is $0.4 and the profit of each kilogram of Deluxe coffee is $0.5, how many kilograms of each type of coffee should be blended to maximize profit? (a) Formulate this optimization problem as a Linear Programming Problem: () State the decision variables. x1=number of kg of Super brand and x2=number of kg of Deluxe brand x1=number of kg of Brazilian coffee, x2=number of kg of Colombian coffee and x3=number of kg of Kenyan coffee Z= (iii) What is the aim of optimization? max (iv) State the constraints of the Linear Programming Problem. Use notation N/A for unused lines. (Brazilian coffee) (Colombian coffee) (Kenyan coffee) (Super brand) (Deluxe brand) (v) State the sign restrictions for decision variables. (v) State the sign restrictions for decision variables. (b) Show the feasible region, find all extreme points, and solve the problem graphically: (i) How many extreme points (vertices of the polygon), including the origin, has the feasible region? (ii) Which of the points are extreme points? (0,0) (18,0) (0,18) (15,6) (9,12) (13.5,9) (27,0) (0,21) (ii) Write the optimal value of the objective function. (c) Use graphical sensitivity analysis to show that if the profit of each kilogram of Deluxe coffee is between $0.4 and $0.6, the current basis remains optimal: (i) State the slope of each binding constraint in increasing order? m1= m2= (ii) What is the current slope of the objective function? mz= (d) What would be the new optimal solution if the profit of each kilogram of Deluxe coffee is $0.65? (0) What is the new value of the objective function? z=$ (ii) What are the values of the decision variables? x1 = (e) What is the shadow price for Colombian coffee? Please answer all parts of the question. Next 120 marks] Problem 1. A coffee packer blends Brazilian coffee, Colombian coffee and Kenyan coffee to prepare two products: Super and Deluxe brands. Each kilogram of Super coffee contains 1/3 kg of Brazilian coffee, 1/3 kg of Colombian coffee and 1/3 kg of Kenyan coffee, whereas each kilogram of Deluxe coffee contains 1/6 kg of Brazilian coffee, 1/3 kg of Colombian coffee and 1/3 kg of Kenyan coffee. The packer has 6 kg of Brazilian coffee, 7 kg of Colombian coffee and 9 kg of Kenyan coffee on hand. If the profit of each kilogram of Super coffee is $0.4 and the profit of each kilogram of Deluxe coffee is $0.5, how many kilograms of each type of coffee should be blended to maximize profit? (a) Formulate this optimization problem as a Linear Programming Problem: () State the decision variables. x1=number of kg of Super brand and x2=number of kg of Deluxe brand x1=number of kg of Brazilian coffee, x2=number of kg of Colombian coffee and x3=number of kg of Kenyan coffee Z= (iii) What is the aim of optimization? max (iv) State the constraints of the Linear Programming Problem. Use notation N/A for unused lines. (Brazilian coffee) (Colombian coffee) (Kenyan coffee) (Super brand) (Deluxe brand) (v) State the sign restrictions for decision variables. (v) State the sign restrictions for decision variables. (b) Show the feasible region, find all extreme points, and solve the problem graphically: (i) How many extreme points (vertices of the polygon), including the origin, has the feasible region? (ii) Which of the points are extreme points? (0,0) (18,0) (0,18) (15,6) (9,12) (13.5,9) (27,0) (0,21) (ii) Write the optimal value of the objective function

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