Question 959083: Solve the linear programming problem by the method of corners.
Minimize C = 4x + 3y
subject to x + y ≤ 48
x + 3y ≥ 60
9x + 5y ≤ 320
x ≥ 10, y ≥ 0
What is the minimum C? What is the point (X,Y)?
Found 3 solutions by Theo, ValerieDavis, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Solve the linear programming problem by the method of corners.
Minimize C = 4x + 3y
subject to x + y ≤ 48
x + 3y ≥ 60
9x + 5y ≤ 320
x ≥ 10, y ≥ 0
What is the minimum C? What is the point (X,Y)?
solve for y in the constraint equations.
you get:
x + y <= 48 becomes y <= (48 - x)
x + 3y >= 60 becomes y >= (60 - x)/3
9x + 5y <= 320 becomes y <= (320 - 9x) / 5
you also have the additional constraints of x >= 10 and y >= 0.
you will graph the equality portion of these constraints and then you will fill in the area that satisfies all the inequality portions of the constraints.
your graph will look like this:
the corner points of your feasible region are:
(10,38)
(20,28)
(10,16 and 2/3)
(30,10)
you evaluate your objective function of 4x + 3y at each of these corner points.
you will find that the minimum solution is at the point (10, 16 and 2/3) where the value of 4x + 3y is equal to 90.
Answer by ValerieDavis(6)  (Show Source):
You can put this solution on YOUR website! Great solving linear programming homework! I studied Linear programming in my master's degree in industrial and systems engineering. It helped me to revise and quick wrap up the important concepts in operation research subject.
Answer by ikleyn(52787)  (Show Source):
You can put this solution on YOUR website! .
Dear ValerieDavis (!)
Please accept my deepest THANKS for so informative message from you (!)
As well as for 6 other your messages to this forum during the past 10 years, that also were highly informative and educative !
It was a true pleasure to me to read every one of them !
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