Application of first-order mathematical inequality and binary linear equations

A farm with 100 employees owns 20 hectares of land and grows rice and cotton respectively (both planting areas are integers). The relevant data are as follows:

The number of people needed per hectare of crops and the cost per hectare of crops

Rice for 4 people and rice for 45,000 yuan.

Cotton 5 people cotton 75,000 yuan

If the estimated gross output value p (ten thousand yuan) meets 105≤P≤ 120, how should this farm arrange the planting area of rice and cotton?

Let the area of rice be x and the area of cotton be y.

X+Y=20

4X+5Y & lt; = 100

105<P=4 .5X Seventh anniversary of the conference. 5Y< 120

105<4.5 +7.5 times (20 times)< 120

105< 150-3x & lt; 120

-45 & lt; -3x & lt; -30

∴ 10<; x & lt 15

X and y are integers, so there are the following schemes:

1)X= 1 1,Y=9, 1 1 * 4+9 * 5 = 89 & lt; 100

2)X= 12,Y = 8; 12 * 4+8 * 5 = 88 & lt; 100

3)X= 13,Y = 7; 13 * 4+7 * 5 = 87 & lt; 100

4)X= 14,Y = 6; 14 * 4+6 * 5 = 86 & lt; 100

(2)

Analysis:

The equivalent relationship is: 400× number of units shipped from Beijing to Wuhan +800× number of units shipped from Beijing to Chongqing +300× number of units shipped from Shanghai to Wuhan +500× number of units shipped from Shanghai to Chongqing =7600. Just substitute the correlation value into the solution.

Answer:

Solution: If Beijing is shipped to Wuhan X, Beijing will be shipped to Chongqing (10-x), Shanghai will be shipped to Wuhan (6-x) and Shanghai will be shipped to Chongqing (x-2).

400 x+800×( 10-x)+300×(6-x)+500×(x-2)= 7600,

The solution is x=6,

∴ 10-x=4,

6-x=0,

x-2=4。

A: Beijing shipped 6 sets to Wuhan, Beijing shipped 4 sets to Chongqing, Shanghai shipped 0 sets to Wuhan and Shanghai shipped 4 sets to Chongqing.