Question

Solve the following LP.P.

Maximize z = 13x + 9y,

Subject to 3x + 2y ≤ 12,

x + y ≥ 4,

x ≥ 0,

y ≥ 0.

Answer 1

Equation	x	y	Points	Side
3x + 2y = 12	0	6	A(0, 6)	Origin
	4	0	B(4, 0)	Side
x + y = 4	0	4	C(0, 4)	Non-origin
	4	0	D(4, 0)	Side

Shaded region is the feasible region ABCA.

Z = 13x + 9y

Z(A) = 0 + 9 × 6 = 54

Z(B) = 13 × 4 + 0 = 52

Z(C) = 0 + 4 × 9 = 36

∴ Max, value of z is 54 at A(0, 6)

i.e., when x = 0,

y = 6.