SOLUTION: Minimize P subject to the following constraints. P = 9y + x x ≥ 0 y ≥ 0 x + y ≥ 3 2y − x ≤ 1 Find the minimum value of P. P= & Find the point where the

Algebra ->  College  -> Linear Algebra -> SOLUTION: Minimize P subject to the following constraints. P = 9y + x x ≥ 0 y ≥ 0 x + y ≥ 3 2y − x ≤ 1 Find the minimum value of P. P= & Find the point where the      Log On


   

Question 1162552: Minimize P subject to the following constraints.
P = 9y + x

x ≥ 0
y ≥ 0
x + y ≥ 3
2y − x ≤ 1
Find the minimum value of P.
P=
&
Find the point where the minimum occurs.
(x,y)=
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52940) About Me  (Show Source):
You can put this solution on YOUR website!
.

At this site, I just created a lesson
    - Solving minimax problems by the Linear Programming method
which teaches the beginner students on how to solve linear minimax problems using the Linear programming method.

Use it and learn the subject from there.



Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


Constraint boundary lines:

y+=+-x%2B3
y+=+%281%2F2%29x%2B%281%2F2%29

Intersection point: (5/3,4/3)

a graph... feasibility region is above the red line and below the green line

graph%28400%2C400%2C-1%2C5%2C-1%2C5%2C-x%2B3%2C.5x%2B.5%29

The only two corners of the feasibility region are (3,0) and (5/3,4/3).

(3,0): P = 9(0)+3 = 3
(5/3,4/3): P = 9(4/3)+5/3 = 41/3

ANSWERS: The minimum value of P is 3, at the point (3,0).