Question

Solve the following LP problem graphically using level curves.

MAX: 7 X1 + 4 X2
Subject to: 2X1 + X2 ≤ 16
X1 + X2 ≤ 10
2X1 + 5 X2 ≤ 40
X1, X2 ≥ 0

a. X1 = 4
b. X1 = 6
c. X1 = 8
d. X1 = 10

Answer 1

option 2

X1=6

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Placing each of the constraints in the graph

to place it we need to make it perfect inequalities and then using zero equal to one variable we can calculate the point for an axis

Like,

for the first constraint

2x1+x2=16

x2=0

2x1=16

x1=8 then the point on the y-axis is (8,0)

x1=0

x2=16 then the point on the x-axis is (0,16)

and so on

Placing this point and joining lines then shading the area lower which is inequalities showing

for positive inequalities (X1 and X2 greater than zero), the solution should be positive quadrant

from the graph the solution is at X1=6 and X2 =4

solution of LPP is

7X1+4X2

7*6+4*4

=58

the solution is 58