Gender: digging holes (person/day), planting trees (person/day) and watering (person/day)

Male 6 20 30 25

Female 5 10 20 15

There are boys digging holes, boys planting trees x2, boys watering x3, girls digging holes y 1, girls planting trees y2 and girls watering y3.

The objective function is to plant as many trees as possible, z=25x3+ 15y3.

So the mathematical model of this problem is

3. Model solving

This is a linear optimization problem, which can be solved by MATLAB software. The best solution is as follows

x 1 = 3.75 x2 = 0x 3 = 2.25y 1 = 0 y2 = 3.75 y3 = 2.25

(Note: The quota allocated to a certain labor force is not necessarily an integer; If 10.5 male students dig holes, it means that 10 male students dig holes all day, 1 male students dig holes for half a day)

4.MATLAB program

c =[0 0-25 0 0- 15]；

a =[]；

b =[]；

aeg=[ 1 1 1 0 0 0

0 0 0 1 1 1

-2 3 0 - 1 2 0

-4 0 5 -2 0 3];

beg =[6； 5; 0; 0];

vlb =[0； 0; 0; 0; 0; 0];

vub =[]；

[x，fval]=linprog(c，a，b，aeg，beg，vlb，vub)

x =

3.7500

0.0000

2.2500

0.0000

3.7500

1.2500

fval =

-75.0000