Mathematical modeling for solving problems;

(1) At the beginning of the fourth quarter, the number of newly recruited nannies in the company was X 1, X2, X3 and X4.

At the beginning of four quarters, the number of nannies is S 1, S2, S3 and S4.

The objective function is to pay the least this year: Min s 1+s2+s3+s4.

s . t 65s 1 & gt； =6000+5X 1

65s2 & gt=7500+5X2

65s3 & gt=5500+5X3

65s4 & gt=9000+5X4

s 1= 120+X 1

s2=0.85s 1+X2

s3=0.85s2+X3

s4=0.85s3+X4

x 1，x2，x3，x4 & gt=0

s 1，s2，s3，s4 & gt=0 ( 1)

(2) At the beginning of the fourth quarter, the number of newly recruited nannies in the company was X 1, X2, X3 and X4.

At the beginning of four quarters, the number of nannies is S 1, S2, S3 and S4.

The number of nannies dismissed at the end of the four quarters is y 1, y2, y3 and y4 respectively.

The objective function is to pay the least this year: Min s 1+s2+s3+s4.

s . t 65s 1 & gt； =6000+5X 1

65s2 & gt=7500+5X2

65s3 & gt=5500+5X3

65s4 & gt=9000+5X4

s 1= 120+X 1

s2=0.85s 1+X2

s3=0.85s2+X3-y2

s4=0.85s3+X4-y3

x 1，x2，x3，x4 & gt=0

s 1，s2，s3，s4 & gt=0(2)