Question

Solve The LP problem using the graphic method

Z Max=6X₁+5X₂

Constaint function:

X₁ + 2X₂ ≤ 240
3X₁ + 2X₂ ≤ 300
X₁≥ 0 , X₂≥0

Answer 1

Given data:

Objective function:

Max, Z=6X1+5X2

Constaint

X1 + 2X2 ≤ 240 ----------(1st constraint)
3X1 + 2X2 ≤ 300  ----------(2nd constraint)
X1≥ 0 , X2≥0

X1 intercepts in ghraph.

X1 = 240 in first constraint

X1 = 100 in second constraint

X2 intercepts in graphs.

X2 = 120 in 1st constraint

X2 =150 in second constraints

then the graph will be

the shaded area is the constraint satisfied area.

point A = (0,120)

point B =(30,105)

point C = (100,0)

These are the boundary points one of this point will give the maximum value.

Z= 6X1+5X2

Z(A) =(6*0)+5*120 = 600

Z(B) = 6*30 +5*105 =705

Z(C) = 6*100+ 5*0 = 600

So we are getting maximum value 705. at B point .

so the answer is

X1 =30

X2 = 105,

Max Z = 705.