Question

The point which provides the optimal solution of the linear programming problem
max z = 45x + 55y
6x + 4y ≤ 120
3x + 10y ≤ 180
x ≥ 0, y ≥ 0
has the coordinates __________.

Answer 1

max_z = 45x + 55y
s.t 6x + 4y ≤ 120
3x + 10y ≤ 180; x, y ≥ 0
Firstly, we will convert the inequalities to equalities
i.e. 6x + 4y = 120, 3x + 10y = 180 and x = 0, y = 0
The feasible region of the L.P.P is shaded region in figure

Points	Value of z = 45x + 55y
O(0, 0)	z = 0
A(20, 0)	z = 45(20) + 55(0) = 900
B(10, 15)	z = 45(10) + 55(15) = 1275
C(0, 18)	z = 45(0) + 55(18) = 990

Therefore optimal solution is given by point (10, 15)