AboutPaul Klarreich Expertise I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction.
I can also try (but not guarantee) to answer questions on Abstract Algebra
-- groups, rings, etc. and Analysis -- sequences, limits, continuity.
I won't understand specialized engineering or business jargon.
Experience I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.
Expert: Paul Klarreich Date: 5/14/2008 Subject: Linear Programming
Question Consider the following linear programming problem
MIN Z = 10x1 + 20x2
Subject to:x1 + x2 >= 12
2x1 + 5x2 >= 40
x2 <= 13
x1 , x2 >= 0
What are the values of x1 and x2 at the extreme points of the feasible region ?
I know that the set of coordinates for the first (1)constraint is x1 = 12 and x2 = 12 (12,12)
second (2nd) constraint is x1 = 20 and x2 = 8 (20,8)
Questioner: Jenna
Category: Advanced Math
Private: No
Subject: Linear Programming
Question: Consider the following linear programming problem
MIN Z = 10x1 + 20x2
Subject to:
x1 + x2 >= 12
2x1 + 5x2 >= 40
x2 <= 13
x1 , x2 >= 0
What are the values of x1 and x2 at the extreme points of the feasible region ?
I know that the set of coordinates for the first (1)constraint is x1 = 12 and x2 = 12 (12,12)
second (2nd) constraint is x1 = 20 and x2 = 8 (20,8)
third constraint (3rd) is X2 = 13 (0,13)
.............................................
Hi, Jenna,
I am afraid what you have there does not make any sense.
..................................
I know that the set of coordinates for the first (1)constraint is x1 = 12 and x2 = 12 (12,12)
second (2nd) constraint is x1 = 20 and x2 = 8 (20,8)
third constraint (3rd) is X2 = 13 (0,13)
............................
What do these sentences say? I don't know. Each constraint defines a region and you want the intersection of them. Normally you will find the 'corners' of the region, then evaluate your Z at each.
Are you sure your constraints are in the right 'sense'? [Meaning '>=' rather than '<='?]
You have:
x1 + x2 >= 12
13 >= x2
---------------
x1 + x2 + 13 >= 12 + x2
x1 + 1 >= 0
x1 >= -1
AND you have
x1 >= 0, which makes that redundant.
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