Question

Explain the process of this problem to approach the correct answer. Thank you

following Linear Programming (LP) Consider the problem. Minimize Z= 4x1 + 2x2 Subject to (soto). 2x1 - x2 x1 + 2x2 X1 + x2 IVAN 1003 and Xizo x220 a. draw the feasible region and the objective function line bo Indicate all Corner point feasible solutions and the optimal Solution.

Answer 1

(a)

x2 2x1 - x2 >= 4 x1 + 2x2 = 8 x1 + x2 >= 4 Objective 0 1 2 3 5 6 7 8 4 x1

The green-shaded area is the feasibility region in this problem.

(b)

Corner point	Intersection between	(x1, x2)	Objective = 4x1 + 2x2
A	2x1 - x2 = 4 and x1 + 2x2 = 8	(16/5, 12/5)	17.60
B	2x1 - x2 = 4 and x1 + x2 = 4	(8/3, 4/3)	13.33 (min)
C	x1 + x2 = 4 and x2 = 0	(4, 0)	16.00
D	x1 + 2x2 = 8 and x2 = 0	(8, 0)	32.00

The objective is minimizex at corner point-B.

So, the optimal solution is x1 = 8/3 and x2 = 4/3 with Min. Z = 13.33