As the picture shows, the pentagon ABCDE is a schematic diagram of a piece of land. The quadrilateral AFDE is rectangular, AE = 130m, ED = 100m, and the BC segment ∠F intersects AF and FD at points re

As the picture shows, the pentagon ABCDE is a schematic diagram of a piece of land. The quadrilateral AFDE is rectangular, AE = 130m, ED = 100m, and the BC segment ∠F intersects AF and FD at points respectively. (1) If the MP intersection AF is extended to point H, then △BHP is an isosceles right triangle.

BH=PH= 130-x

DM = HF = 10-BH = 10-( 130-x)= x- 120

So y=PM? EM=x？ [ 100-(x- 120)]=-x ^ 2+220 x

From 0≤PH≤ 10

We get 120≤x≤ 130, because the symmetry axis of parabola y =-x 2+220x is a straight line x= 1 10, and the opening is downward.

Therefore, in the range of 120≤x≤ 130,

When x= 120, y =-x 2+220x gets the maximum value.

Its maximum value is y= 12000(㎡).

(2) Only when non-resettlement households build houses in resettlement areas can the government resettle all 30 migrant farmers.

From the meaning of the question, get

30× 100+ 120 a≤ 12000×50%

30×4+( 12000-30× 100- 120 a)×0.0 1+90+ 100 2× 10×0.02≤ 150+3a

The solution is181721≤ a ≤ 25.

Because a is an integer.

Therefore, when there are at least 19 non-resettlement households and at most 25 building households in the resettlement area, the government can resettle all 30 outdoor migrant farmers; Otherwise, the government will not be able to resettle all 30 migrant workers.