SOLUTION: 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

Algebra ->  College  -> Linear Algebra -> SOLUTION: 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       Log On


   

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!!!
Answer by Fombitz(32388) 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%28+300%2C+300%2C+-2%2C+10%2C+-1%2C+2%2C+6-x%2C+x-4%29+
.
.
.
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
.
.
.
Min value of P=12 and occurs at (4,0).
Max value of P=20 and occurs at (5,1).
.
.
.
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.