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Advocard [28]
3 years ago
8

George has $49 which he decides to spend on x and y. commodity x costs $5 per unit and commodity y costs $11 per unit. he has th

e utility function u(x, y) = 3x 2 + 6y 2 and he can purchase fractional units of x and y. george will choose
Mathematics
1 answer:
FromTheMoon [43]3 years ago
7 0

We are given the equations:

<span>5 x + 11 y = 49                    --> eqtn 1</span>

<span>u = 3 x^2 + 6 y^2               --> eqtn 2</span>

 

Rewrite eqtn 1 explicit to y:

11 y = 49 – 5 x

<span>y = (49 – 5x) / 11               --> eqtn 3</span>

 

Substitute eqtn 3 to eqtn 2:

u = 3 x^2 + 6 [(49 – 5x) / 11]^2

u = 3 x^2 + 6 [(2401 – 490 x + 25 x^2) / 121]

u = 3 x^2 + 14406/121 – 2940x/121 + 150x^2/121

u = 4.24 x^2 – 24.3 x + 119.06

Derive then set du/dx = 0 to get the maxima:

du/dx = 8.48 x – 24.3 = 0

solving for x:

8.48 x = 24.3

x = 2.87

 

so y is:

y = (49 – 5x) / 11 = (49 – 5*2.87) / 11

y = 3.15

 

Answer:

<span>George will choose some of each commodity but more y than x.</span>

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insens350 [35]

x-3y= 1

The equation needs to be rewritten in proper Slope intercept form ( y = mx+b) where m is the slope and b is the y-intercept.

x-3y = 1

Subtract x from each side:

-3y = 1-x

Divide both sides by -3:

y = 1/-3 - x/-3

Simplify:

y = 1/3x - 1/3

The slope is 1/3

5 0
3 years ago
Solve for x. The triangles in each pair are similar
liubo4ka [24]
9x +1= 0
9x/9 +1-1=0
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3 0
2 years ago
et f(x) = x + |2x − 3|. Find all solutions to the equation f(x) = 12. (Enter your answers as a comma-separated list. If an answe
Alinara [238K]

Answer:

1. {5,-9}

2.{4}

3.{9/2}

Step-by-step explanation:

The equation f(x)=x+\lvert 2x-3 \rvert=12 can be solved as follows:

x+\lvert 2x-3 \rvert =12\,\,\,\text{(given equation)}

\lvert 2x-3 \rvert =12-x

2x-3=12-x\,\,\text{or}\,\,2x-3=-(12-x)

3x=15\,\,\text{or}\,\,\x=-9

Then, the solutions of the equation are x=5, x=-9.

Now, if g(x)=5x-3+\lvert x+4\rvert, we can solve the equation g(a)=4a+9 as follows:

5a-3+\lvert a+4 \rvert =4a+9

\lvert a+4\rvert =4a+9-5a+3

a+4 =-a+12\,\,\text{or}\,\,a+4=-(-a+12)

2a=8\,\,\text{or}\,\,4=12

So, the unique solution of this last equation is a=4

The last equation is h(x-1)=x-3, where h(x)=\lvert x \rvert -2x+5.. To solve this equation we can proceed as follows:

h(x-1)=x-3

\lvert x-1\rvert -2(x-1)+5=x-3

\lvert x-1 \rvert -2x+2+5=x-3

\lvert x-1\rvert =3x-10

x-1=3x-10\,\,\text{or}\,\,x-1=-(3x-10)

-2x=-9\,\,\text{or}\,\,4x=11

x=9/2\,\,\text{or}\,\,x=11/4

But, x=11/4 is not a solution of this equation. So the unique solution is x=9/2.

8 0
2 years ago
The temperature in the morning was−8 °F. The temperature dropped 13 degrees by night. What is the temperature at night?
Firlakuza [10]

Answer:

-21 degrees

Step-by-step explanation:

-8+(-13)=-21

7 0
2 years ago
The circumference of a circle is 3π in. What is the area of the circle? ​ 1.5π ​ in² ​ 2.25π ​ in² ​ 6π ​ in² ​ 9π ​ in²
dangina [55]
C = 2<span>πr
so
r = C/2</span><span>π
r = 3</span>π/2<span>π
r = 3/2
r = 1.5

A = </span><span>πr^2
A = </span><span>π(1.5)^2
A = 2.25</span><span>π 

answer
</span><span>2.25π ​ in²</span>
3 0
3 years ago
Read 2 more answers
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