Maximize z=2x+4y
 subject to x+4y ≦ 18
 4x+2y ≦ 16
 x ≧ 0
 y ≧ 0

We form the equations of graphs of the boundary lines
lines by replacing the inequality symbols by equal 
signs.

x+4y = 18    <---line thru points (0,4.5) and (6,3) 
4x+2y = 16   <---line thru points (4,0) and (0,8)
x = 0        <---the y-axis 
y = 0        <---the x-axis



We evaluate the objective function to maximize
at each corner point:

Corner     z = 2x+4y
 (0,0)     z = 2(0)+4(0) = 0      <---minimum value
 (0,4.5)   z = 2(0)+4(4.5) = 18
 (2,4)     z = 2(2)+4(4) = 20     <---maximim value
 (4,0)     z = 2(4)+4(0) = 8

The maximum value of z is 20, and will occur at (2,4), when x=2 and y=4

Edwin

Maximize z=2x+4y
 subject to x+4y ≦ 18
 4x+2y ≦ 16
 x ≧ 0
 y ≧ 0

We form the equations of graphs of the boundary lines
lines by replacing the inequality symbols by equal 
signs.

x+4y = 18    <---line thru points (0,4.5) and (6,3) 
4x+2y = 16   <---line thru points (4,0) and (0,8)
x = 0        <---the y-axis 
y = 0        <---the x-axis



We evaluate the objective function to maximize
at each corner point:

Corner     z = 2x+4y
 (0,0)     z = 2(0)+4(0) = 0      <---- minimum value
 (0,4.5)   z = 2(0)+4(4.5) = 18
 (2,4)     z = 2(2)+4(4) = 20     <---- maximum value
 (4,0)     z = 2(4)+4(0) = 8

The maximum value of z is 20, and will occur at (2,4), when x=2 and y=4

Edwin