Question

Minimise and Maximise
z = 2x + 6y
Subject to the constraints:
x + 2y < 10, x + y = 7, x > 2, x > 0,y > 0​

Answer 1

Answer:

x≤0

When x is greater than zero it mean tangent of that mean the feasible region is on or to the right of the line where equation is zero(x=0) which is the line which is y axis

y≤0

Where y is greater that it means above that mean feasible region is on or above the line where equation is y=0 which is the line which is x-axis

Those two mean that the feasible region is in the upper right hand part of the xy co ordinate system.

See image 1

When x is greater that it mean right of

y≤1−x

That mean feasible region os on or of above the line where equation is x+y=1

See image 2

3x+2y≤6

If we solve

x≤

3

6−2y

y≤

2

6−3x

xintercept(2,0)yintercept(0,3)

Cornerpointvalueof2=2x+4y

(1,0)2=2(1)+4(10)=2+0=2

(2,0)2=2(2)+4(0)=4+0=4

(0,3)2=2(0)+4(3)=0+12=12

(0,1)2=2(0)+4(1)=0+4=4

Maximum value when x=0y=3