A manufacturing company makes two models A and B of a product. Each piece of Model A requires 9 labour hours for fabricating and 1 labour hour for finishing. Each piece of Model B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs. 8000 on each piece of Model A and Rs. 12000 on each piece of Model B.

a) Define all the variables.

(01 points)

b) Write a linear programming model. (03 points)

c) Solve the problem using the corner point method. (04 points)

d) What is the maximum profit per week? (02 points)

e) Suppose for finishing, the maximum labour hours available is 31. Calculate how much more profit will gain by increasing the labour hours from 30 to 31 for finishing. (05 points)

f) Calculate the optimality range. (02 points)

g) Suppose that the unit profit for Model A and Model B are changed to 8000 + 6000" and 12000 + 30000, respectively. Will the current optimal solution remain the same?