Questions on Algebra: Linear Algebra (NOT Linear Equations) answered by real tutors!

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Question 163239: How would you find the maximum and minimum values, if they exist, of the objective function for the given constraints?:
P=5y+3x
Constraints:
x+y<6
x-y<4
x>0
y>0

Thank you!!!: How would you find the maximum and minimum values, if they exist, of the objective function for the given constraints?:
P=5y+3x
Constraints:
x+y<6
x-y<4
x>0
y>0

Thank you!!!
Answer by Fombitz(1798) About Me  (Show Source):
You can put this solution on YOUR website!
When you plot you constraints, your feasible region is triangular patch with vertices at (4,0),(6,0),and (5,1).
graph( 300, 300, -2, 10, -1, 2, 6-x, x-4)
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The min and max values will occur at the vertices.
P(4,0)=5(0)+3(4)=12
P(6,0)=5(0)+3(6)=18
P(5,1)=5(1)+3(5)=20
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Min value of P=12 and occurs at (4,0).
Max value of P=20 and occurs at (5,1).
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Since the inequalities do not include the lines (">" and "<" and not "<=" and ">=", these values for P are limits for P and are not obtained in the feasible region.