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).
Answers
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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
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