a) Solve the following linear program graphically using an iso-cost/iso-profit

line. The vertices (corners) of the feasible region should be clearly labelled A,B,C etc.

Minimise z = 2y - 3x

Subject to 2x + y 10 Constraint 1

x + y 12 Constraint 2

x 3y -6 Constraint 3

x,y 0

Copy the tables shown below into your answer book and fill in the values required. (21 marks)

	Optimal value (4dp)	Opportunity cost (4dp)
x
y
z

	Shadow price (4dp)
Constraint 1
Constraint 2
Constraint 3

(b) If constraint 3 now becomes x 3y = -6 then copy the tables shown below into your answer book and fill in the values required. Clearly explain how you decided the values you have entered in these tables. (4 marks)

	Optimal value (4dp)	Opportunity cost (4dp)
x
y
z

	Shadow price (4dp)
Constraint 1
Constraint 2