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.