Question

Using Simplex method, maximuze Z= 3x +5y subject to constraints
3x + 2y < 18, x < 4, y < 6 and x, y > 0.​

Answer 1

Answer:

Shaded portion OABCD is the feasible region,

Where O(0,0), A(7,0), D(0,6)

For B:

3x+y=21....(i)

x+y=9......(ii)

Subtract (ii) from (i) we get

3x+y−x−y=21−9

2x=12

x=6

y=9−6=3

∴B(6,3)

For C:

x+y=9....(iii)

x+4y=24......(iv)

Subtract (ii) from (i) we get

x+y−x−4y=9−24

−3y=−15

y=5

x=9−5=4

∴C(4,5)

Z=3x+5y

Z at O(0,0)=3(0)+5(0)=0

Z at A(7,0)=3(7)+5(0)=21

Z at B(6,3)=3(6)+5(3)=33

Z at C(4,5)=3(4)+5(5)=37

Z at D(0,6)=3(0)+5(6)=30

Thus, Z is maximized at C(4,5) and its maximum value is 37.