Question

Consider the linear programming problem: Minimize Z = 3x + 9y Subject to the constraints: x + 3y < 60 x + y > 10, x < y, x > 0, y > 0 

(i) Draw its feasible region. 

(ii) Find the vertices of the feasible region 

(iii) Find the minimum value of Z subject to the given constraints.

Answer 1

(i) 

(ii) The feasible region is ABCD.

Solving x + y = 10, x = y we get B(5, 5) 

Solving x + 3y = 60, x = y we get C(15, 15) 

Hence the comer points are A(0, 10) , B(5, 5), C(15, 15), D(0, 20) 

(iii) Given; Z = 3x + 9y

Corner points	Value of Z
A	Z = 3(0)+9(10) = 90
B	Z = 3(5)+9(5) = 60
C	Z = 3(15)+ 9(15) = 190
D	Z = 3(0)+9(20) = 180

Form the table, minimum value of Z is 6 O at B(5, 5).