The goal is
Max 3x+5y +7z
The constraints that need to be met are
x+2y+3z & lt; = 18
2x+y+3z & lt; = 100
x + y + z = 10
x & gt= 0
y & gt= 0
z & gt= 0
An optimal solution can be obtained by solving the above problems with simplex method.
x = 2
y = 8
z = 0
The total value is as high as 46.
If you don't use simple methods, this problem can also be solved by drawing:
Substituting z = 10-x-y into the above problem, we can get
Maximum 70-4x-2y
The constraints that need to be met are
2x+y & gt; = 12
x+2y & gt; = -70 (this condition is redundant and can be deleted)
x+y & lt; = 10
x & gt= 0
y & gt= 0
Drawing an image on a two-dimensional plane shows that
The optimal solutions satisfying the conditions are all on the line 2x+y = 12 (2).
Recombination x, y, z y and z must be integers.
Finally, the optimal solution can be obtained.
x=2,y=8,z=0
or
x=3,y=6,z= 1
or
x=4,y=4,z=2
or
x=5,y=2,z=3
or
x=6,y=0,z=4
The maximum total value is 46.