A function synthesis within half an hour

1.According to the total quantity of three vegetables of 84 tons, the analytical formula of the function can be obtained: +2(40-x-y)=84, i.e. + = 4

2.Value range:

No less than 4 cars are to be shipped for each type of vegetable: x 4, y 4, 40-x-y 4, and the weight of the vegetables in the shipment b does not exceed the sum of the weights of the two vegetables in the shipment a c: +2 (40-x-y).

i.e.: x 4, y 4, x + y 36, - of course x, y are integers.

The next step is to solve this optimization problem, use what you have learned to do the math yourself!

1. There are (40 x y) cars for shipment C.

y=40-2x

2. List the inequality groups according to the title:

1) The number of vehicles transporting A is not less than 4: x 4

2), the number of vehicles transporting B is not less than 4: y = 40-2x 4, solution x 183), the weight of transporting B vegetables does not exceed the sum of the weight of shipping A and C vegetables: , solution x 10

Therefore, the value range of x is 10 x 18

3. Profit: w substitute y=40-2x, w 672

When x takes the minimum value of 10, w has a maximum value of 568

A: 10 cars, 22 tons, profit 132 yuan.

B: 20 cars, 42 tons, profit 336 yuan.

C: 10 cars, 20 tons, profit 100 yuan.

1) Because a b is loaded x y cars, so c (40-x-y) cars can be listed by the title:

The solution yields y=40-2x

2) Again from the question: x 4

y 4 and above y=40-2x

Can be solved: 40-2x 4

2x≤36x≤18 2x=40-y

x=20-1/2y

20-1/2y≥4

1/2y≤16

y 32x 10 so the final result: 10 x 18

4≤y≤32

3) In fact, there are as many cars that transport C as there are cars that transport A, because 40-(x+y).

40-(x+40-2x)

40-x-40+2x

x then the equation for column profit is easier: w=

So the smaller the x, the greater the profit, so x takes 10

At this point, the profit w=

.2x+

y=40-2x

2)、x≥4

40-2x≥4

x can be an integer in the range of 10 x 18.

3) w When x=10, w has a maximum value of 568

1) y=40-2x

2) x is greater than or equal to 4 and less than or equal to 18

3) w=40-x-y)*5= x=4 w=4 w=4 w=4 w=4 w=4 w=4 w=4 w=4 w=4 w=4 w=4 w=4

Let y=kx+b

Bring in (-2,7)(0,3).

7=-2k+b

3=b ∴k=-2 b=3∴y=-2x+3

When x=, y=2

So in a straight line.

Remember that the characteristics of the primary function are that the extremum of x corresponds to the extremum of y, that is, y=10 when x=0, y=30 when x=10, or y=30 when x=0, and y equals 10 when x=10

Let y=ax+b bring (0,10) and (10,30) into the solution, a=2, b=10

Bring (0,30) and (10,10) into the solution a=-2 b=30, so the function is analytically y=2x+10 or y=-2x+30, will it be?? If you don't understand, ask me again.

Let y=ax+b bring (0,10) and (10,30) into the solution, a=2, b=10

Bring (0,30) and (10,10) into the solution and get a=-2 b=30

So the analytic formula of the function is y=2x+10 or y=-2x+3

1）e（a，1-a） f（1-b，b）

2)(b-a-1)/2

Subtract the area of the triangle OAE from the area of the triangle OAF to get the area of the triangle OEF.

y=k1x+b has an intercept of 2 on the y-axis, then b=2

Substituting (-2,4) yields k1=-1 k2=-2, then y=-1x+2 y=-2x

If the line y=-1x+2 intersects (2,0) with the x-axis, the area is 1 2 * 2 * 4 = 4

From the intercept on the y-axis is 2, we get: b=2, and then bring in (-2,4) to get 4=-2k1+2,4=-2k2, and k1=-1,k2=-2

The area is: 1 2*2*4=4

Draw y=5x+4 and y=2x+10 in the same coordinate system to count the abscissa of the intersection points, which is x=2

5x+4<2x+10, y=5x+4 is below y=2x+10, and below y=2x+10, it is to the left of the intersection.

So it's x<2

3x-6＜0

Let y=3x-6

Draw an image with y=3x-6.

Observe what value is taken in Figure x, 3x-6 0

This is the range of x values.

Establish a Cartesian coordinate system, then draw the image of these two straight lines, find the intersection coordinates (2, 14) and then mark the upper part of the image of the straight line y=2x+10, and the interval where this x is located is the interval sought.

a(0,-1),b(5,0), let p(x,k x)

Because PAB is an isosceles right triangle, PB=PASo:

x-5)^2+(k/x-0)^2=(x-0)^2+(k/x+1)^2...1)

And because it is perpendicular, the slope product = -1, i.e.

k/x+1)/(x-0)]*k/x-0)/(x-5)]=-1...2)

The rest is to solve the equation.