A question about western economics: a person who earns 120 yuan a week and spends all his money on X and Y commodities has a utility function of u = XY, PX = 2 yuan and py = 3 yuan How many units of X and y will he buy for maximum utility? (2) What are the marginal utility and the total utility of money? (3) If the price of x increases by 44% and the price of Y remains unchanged, how much more income must be increased to keep its original utility level? The sooner the better... We'll offer an additional reward of 100 by 8 o'clock tomorrow

A question about western economics: a person who earns 120 yuan a week and spends all his money on X and Y commodities has a utility function of u = XY, PX = 2 yuan and py = 3 yuan How many units of X and y will he buy for maximum utility? (2) What are the marginal utility and the total utility of money? (3) If the price of x increases by 44% and the price of Y remains unchanged, how much more income must be increased to keep its original utility level? The sooner the better... We'll offer an additional reward of 100 by 8 o'clock tomorrow

According to MUX / PX = muy / py, Y / x = PX / py = = = > x · PX = y · py
And X · PX + y · py = 120 = = = > x · PX = y · py = 60 * 1
So, x = 60 / Px, y = 60 / py
X = 30, y = 20
Total utility 30 * 20 = 600
Marginal utility I really haven't read for several years. I forgot how to find the derivative. I think the marginal utility of money is 10
X price up 44%
PX=2.88
*88 y = Z / 3
In addition, X * y z ^ 2 / (2.88 * 3) = 600
Z=72
Therefore, the original effect can be achieved only when the salary becomes 144 yuan

The solution of the system of equations ax + by = a + B BX + ay = a + B ab ≠ 0 | a | B with respect to XY|

The results show that: (a + b) (x + y) = 2A + 2B, x + y = 2
Subtracting: (a-b) (X-Y) = 0, because ab ≠ 0 | a | B |, so A-B ≠ 0, so X-Y = 0,
x=y=1

On two systems of equations of XY

The first solution is x-2y = 5
3x+2y=7
Add
4x=12
x=3,y=(x-5)/2=-1
Put in the other two
3a-b=-7
3b-a=-1
a=3b+1
Substituting 3a-b = - 7
9b+3-b=-7
b=-5/4
a=3b+1=-11/4

Given that a is an integer and X, y is the integer solution of the equation x ^ 2-xy-ax + ay + 1 = 0, find the value of X, y
It can't be just the result - should it be factorized?
People on the first floor, would you please be more detailed?

x^2-xy-ax+ay+1=(x^2-xy)-(ax+ay)+1=x(x-y)-a(x-y)+1=(x-y)(x-a)-1=0
That is, (X-Y) (x-a) = - 1
Because x, y, a are integers
So X-Y = 1, x-a = - 1 or X-Y = - 1, x-a = 1
So x = A-1, y = A-2 or x = a + 1, y = a + 2

Given that a is an integer, X and y are the integral solutions of the equation x-xy-ax + ay + 1, find X-Y

x^2 - xy -ax +ay +1
= x(x-y)-a(x-y) +1
=(x-a)(x-y)+1=0
(x-a)(x-y) =-1
Since it's an integer equation, then there is
X-Y = plus or minus 1

Given that a is an integer and X, y is the integer solution of the equation x2-xy-ax + ay + 1 = 0, then X-Y=______ Or______ ．

The result is: X (X-Y) - A (X-Y) + 1 = 0, (X-Y) (x-a) = - 1, ∵ x, y, a are integers, ∵ X-Y = 1 or - 1, so the answer is - 1; 1

Find ∫ ∫ arctan (Y / x) d σ, where the integral region is the closed region bounded by x2 + y2 = 4, X2 + y2 = 1 and the straight line y = 0, y = x in the first quadrant
Note: polar coordinates are required
I can completely convert to polar coordinates, mainly because I can't integrate

x=r cosθ
Y = R sin θ (θ from 0 to π / 4; R from 1 to 2; integral region is a sector)
Then the integrand function arctan (Y / x) = arctan [(r sin θ / (r cos θ)] = arctan Tan Tan θ = θ
∫∫arctan(y/x)dσ
=∫ (from 0 to π / 4) d θ∫ (from 1 to 2) r · θ Dr
=∫ (from 0 to π / 4) [(1 / 2) R ^ 2 | (from 1 to 2)] · θ D θ
=∫ (from 0 to π / 4) (3 / 2) θ D θ
=(3 / 2) · (1 / 2) θ ^ 2 | (from 0 to π / 4)
=3π^2/64

Finding the total differential of higher mathematics z = arctan (1 / x + y)

əz/əx = (-1/x²) / [ 1+ (1/x+y)²]
əz/əy = 1/ [ 1+ (1/x+y)²]
dz = əz/əx dx + əz/əy dy = ...

Given that f (x) = x2 + BX + C is an even function, the curve y = f (x) passes through point (2,5), G (x) = (x + a) f (x). (1) find the tangent of the curve y = g (x) with slope 0, find the value range of real number a; (2) if the function y = g (x) reaches the extreme value when x = - 1, determine the monotone interval of y = g (x)

(1) ∵ f (x) = x2 + BX + C is even function, so f (- x) = f (x) has (- x) 2 + B (- x) + C = x2 + BX + C solution, B = 0 and curve y = f (x) passes through point (2,5), 22 + C = 5, C = 1 ∵ g (x) = (x + a) f (x) = X3 + AX2 + X + A, so G '(x) = 3x2 + 2aX + 1, curve y = g (x) has

Let f (x) be a differentiable even function on R and satisfy f (x-1) = - f (x + 1), then the slope of the tangent of the curve y = f (x) at point x = 2014 is

F (x-1) = - f (x + 1) replace x with x + 1 to get f (x) = - f (x + 2) and then replace x with x + 2 to get f (x + 2) = - f (x + 4) to get f (x) = f (x + 4) to get t = 4, so f (2014) = f (2) and f '(2) = f' (2014) f (x) = - f (x + 2) = f (- x), so the function is symmetric with respect to (1,0) to get f '(...)