Question
Constraints{x>=0 y>=0 y<=1/5x+2 5>=y+x objective function: C=7x-3y
(2.5,2.5)
(0,2)
(0,0)
(5,0)
(2.5,2.5)
(0,2)
(0,0)
(5,0)
Answers
GPT-4
We can find which of these points is optimal (maximizes or minimizes the objective function) by plugging each into the objective function (C = 7x-3y) and determining which yields the highest value.
For the point (2.5,2.5),
C = 7(2.5) - 3(2.5) = 10
For the point (0,2),
C = 7(0) - 3(2) = -6
For the point (0,0),
C = 7(0) - 3(0) = 0
For the point (5,0),
C = 7(5) - 3(0) = 35
The point (5,0) yields the highest value (C = 35), therefore it is the point that optimizes the objective function.
For the point (2.5,2.5),
C = 7(2.5) - 3(2.5) = 10
For the point (0,2),
C = 7(0) - 3(2) = -6
For the point (0,0),
C = 7(0) - 3(0) = 0
For the point (5,0),
C = 7(5) - 3(0) = 35
The point (5,0) yields the highest value (C = 35), therefore it is the point that optimizes the objective function.