The maximum value of p is 6 at (2,2).
How to maximize objective function.
Given
Maximize p = x + 2y
Subject to:
x + 6y <= 14
4x + y <= 10
x >= 0
y >= 0
The solution involves finding the values of x and y that maximize p while satisfying the given constraints.
Let's solve graphically
The feasible region defined by the constraints on a graph is the area where all the shaded region of the lines overlap.
The corner points of the feasible regions are:
(0,0), (2,2), (0,2.4) and (2.42,0)
Evaluate p at each corner point.
Maximize p = x + 2y
At (0,0)
p = 0
At (2,2)
p = 2 + 2(2) = 6
At (0,2.4)
p = 0 + 2(2.4) = 4.8
At (2.42,0)
p = 2.42 + 0 = 2.42.
The maximum value of p is 6 at (2,2).