Question

The corner points of feasible region of LPP are (0,8), (4,10), (6,8), (6,5),
(0,0) and (5,0). Let the objective function be z = 3x - 4y. Answer the
following:
(a) Find the point at which minimum value of z occurs.
Cay Find the point at which maximum value of z occurs.
e Find the sum of minimum value of z and maximum value of z.
(d) Let z = px + cy, where p, q> 0
qy
Find the relation between p and q, so that minimum of z occurs at
(0,8) and (4,10).​

Answer 1

Answer:

a.) at (0,8) i.e -32

b.) at (6,5) i.e -2

c.) sum = -37-2 = -39

d.) 4p +2q = 0

Step-by-step explanation:

z = 3x - 4y , now

putting point (i) , z = 3(0) - 4(8) = -32 (minimum)

similarly at 2nd point ( 4 , 10) , z = - 28

at point (6,8) , z= -14

at point (6,5) , z= -2 (maximum)

now z = px + cy given minimum value at (0,8) & (4,10)

so p(0) + q(8) = p(4) + q(10)

8q = 4p + 10q

4p + 2q = 0