Answer:
x = 250
y = 125
u(x,y) = 3125500
Step-by-step explanation:
As given,
The utility function u(x, y) = 100xy + x + 2y
= 2 ,
= 4
Now,
Budget constraint -
x +
y = 1000
⇒2x + 4y = 1000
So,
Let v(x, y) = 2x + 4y - 1000
Now,
By Lagrange Multiplier
Δu = Δv
⇒< 100y + 1, 100x + 2 > = < 2, 4 >
By comparing, e get
100y + 1 = 2 ........(1)
100x + 2 = 4 .........(2)
Divide equation (2) to equation (1) , we get

⇒2(100y+1) = 1(100x+2)
⇒200y + 2 = 100x + 2
⇒200y = 100x
⇒2y = x
Now,
As 2x + 4y = 1000
⇒2x + 2(2y) = 1000
⇒2x + 2x = 1000
⇒4x = 1000
⇒x = 250
Now,
As 2y = x
⇒2y = 250
⇒y =
= 125
∴ we get
x = 250
y = 125
Now,
u(250, 125) = 100(250)(125) + 250 + 2(125)
= 3125000 + 250 + 250
= 3125000 + 500
= 3125500
⇒u(250, 125) = 3125500
Answer:
3
Step-by-step explanation:
if you have 5 plates and you subtract 2 then you have 3 plates left
5-2=3
2/5=0.4
a. 5/2=2.5
b. 4/8=0.5
c. 13/32.5=0.4
d. 18/21=0.857
Answer: Option <span>c. 13 cups juice to 32.5 water</span>
You need to move it 9 times to the left so that there is a value between 1-9 on the left
Negative 4 is less than x because x is one and negative 4 is less than 1