Re: MQE 2013 QUESTION 26

[VR]

could any one plz solve this

26. The minimum value of the objective function z = 5x+ 7y, where x ≥ 0 and y ≥ 0, subject to the constraints
2x + 3y ≥ 6, 3x − y ≤ 15, −x + y ≤ 4 , and 2x + 5y ≤ 27
is
(A) 14,
(B) 15,
(C) 25,
(D) 28

[Sinistral]

is the ans 14 ?

[VR]

yes exactly !, how you did?  Plz explain.

[Sinistral]

plot all the four given inequalities, seeing where they intersect at x and y axis.
the region encompassed by these 4 inequalities becomes a quadrilateral.

plot the objective func and observe when exactly will it remain inside that quadrilateral:
that func will cut y axis at z/7 and x axis at z/5

in order to remain it inside that quadrilateral following 2 conditions must be satisfied (seen from graph only):
2< (z/7) <4
3< (z/5) <5

solving & combining the above two gives: 14<z<25
hence min(z) =14

[VR]

are the coordinates of quadrilateral (0,5.4),(3,0), (13.5,0) and( 0,2).

can we also evaluate the min value by putting these values  into objective function

[Sinistral]

its difficult to explain this without the graph.
but still:
dont look for the 4 corners of the quadrilateral.
after plotting the 4 inequalities the 4 points of interest which we get are: (0,2),(0,4),(3,0),(5,0)

[VR]

Thanks a lot :)

[laracroft]

Hi.
could someone help me with Q 15 of the same sample paper isi 2013 ???