The bottles of perfume and skin care products of Company B are 70-x, 30-(40-x) = x- 10 respectively.
w = 180 x+200(40-x)+ 160(70-x)+ 150(x- 10)=-30x+ 17700。
Therefore, the functional relationship between the total profits W and X of Company A and Company B is W =-30x+ 17700.
(2) The profit of Company A is 180x+200(40-x)=8000-20x,
The profit of Company B is:160 (70-x)+150 (x-10) = 9700-10x.
8000-20x-(9700- 10x)=- 1700- 10x < 0，
Therefore, the profit of Company A will not be higher than that of Company B. 。
(3)from( 1):x≥040-x≥070-x≥0x- 10≥0？ ,
Solution: 10≤x≤40,
W =-30x+17700 ≥17370:
x≤ 1 1，
∴ 10≤x≤ 1 1，
∴ Through two different distribution schemes.
① When x= 10, the head office distributed perfume 10 bottles, 30 bottles of skin care products, 60 bottles of perfume and 0 bottles of skin care products to Company A. 。
(2) When x= 1 1, the head office allocated to Company A perfume 1 1 bottle, 29 bottles of skin care products, 59 bottles of perfume and skin care products 1 bottle.