Question

Solve the following LP model using the corner point method.

Min 4X_1+5X_2

S.T. X_1+2X_2?80

3X_1+X_2?75

X_1,X_2?0

List all the corner points and provide the optimal solution for full credit.

Answer 1

.Objective Function, Min(4x1+5x2)

S.T

x1+2x2 ?80 -----1

3x1+x2 ?75 ---2

x1?0 -----3

x2 ?0 ----4

Pint of Intersection of 1 & 2

x1+2x2 = 80 ---- 4

3x1+x2 = 75 ----5

2*e.q5- eq4

=> 5x1= 150-80 =70

=> x1 = 70/5 = 14

Putting x1 =14 in eq 5

x2 = 75-42 = 33

Point of intersection(14,33)

Point of intersection of other lines are

(0,40) ,(80,0) ,(0,75) & (25,0)

Graph

Corner Points in the feasibility area are

(0,75) , (14,33) and (0,80)

Put the corner points value in objective function

at (0,75)

4x1+5x2 = 4*0+5*75 = 375

At (14,33)

4x1+5x2 = 4*14+5*33 = 221

At (80,0)

4x1+5x2 = 4*80+5*0= 320

Minimum Value of objective function is at (14,33)

so , optimal solution is x1= 14 & x2 = 33

and Optimal Value = 221