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Solution to Question B of 20 12 Mathematical Modeling Competition for College Students in Hubei University of Economics
Solution:

C(i) is used to express the relationship between the number of salespeople in a certain market and their income.

Xi represents the number of salespeople in a certain market,

The total income of the dispatch plan is:

c 1(x 1+ 1)+C2(x2+ 1)+c 1(x3+ 1)+C4(x4+ 1)①

The question is:

exist

x 1 + x2 + x3 + x4 = 8 ②

Under the constraint of ...,

Find the maximum value of ①.

The following is a MATLAB solution program, which can also be easily converted into other languages.

Relationship between sales staff number and income in% market

c 1 =[20 34 48 66 7 1 80 9 1 104 1 10];

C2 =[30 40 54 70 84 90 103 1 10 120];

C3 =[33 38 52 82 95 99 1 10 122 135];

C4 =[40 50 63 97 105 1 12 134 144 150];

n = 8; Percentage of marketers

max = 0; Initial value of maximum gross income percentage

For x 1 = 0:n

For x2 = 0:n

For x3 = 0:n

x4 = n-(x 1+x2+x3);

If x4 & gt=0

Total = c1(x1+1)+C2 (x2+1)+c1(x3+1)+C4 (x4+1).

If the total & gt= maximum

Max = total;

z 1 = x 1; z2 = x2z3 = x3z4 = x4

end

end

End, end, end

Maximum percentage maximum gross income

X = [z 1,z2,z3,z4]%