1.
Solve ln (4x − 5) = 7. Round to the nearest thousandth.


275.408


1,091.633


1,097.883


272.908

Answers

Answer 1

Answer:

Step-by-step explanation:

ln(4x-5)=7

e^(ln(4x-5))=e^7

4x-5=e^7

4x=e^7+5

x=(e^7+5)/4

x=275.408


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A person has utility function u(x, y) = 100xy + x + 2y. Suppose that the price per unit of x is $2, and that the price per unit of y is $4. The person receives $1 000 that all has to be spent on the two commodities x and y. Solve the utility maximization problem

Answers

Answer:

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Step-by-step explanation:

As given,

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100x + 2 = 4        .........(2)

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                   = 3125000 + 250 + 250

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The utility function is given as:

[tex]U(x,y) = 100xy + x + 2y[/tex]

The prices per unit are also given as:

[tex]P_x = 2[/tex]

[tex]P_y = 4[/tex]

When a person receives $1000, then the budget function is:

[tex]2x + 4y = 1000[/tex]

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[tex]x + 2y = 500[/tex]

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[tex]U'(x) = P_x[/tex] and [tex]U'(y) = P_y[/tex]

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[tex]\frac{100y + 1}{100x + 2} = \frac 12[/tex]

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Recall that:

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Divide through by 4

[tex]y=125[/tex]

Recall that:

[tex]x = 2y[/tex]

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[tex]x = 2 \times 125[/tex]

[tex]x = 250[/tex]

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[tex]U(x,y) = 100xy + x + 2y[/tex]

Substitute the values of x and y, in the above function

[tex]U(250,125) = 100 \times 250 \times 125 + 250 + 2 \times 125[/tex]

[tex]U(250,125) = 3125500[/tex]

Hence, the maximized value of the utility function is 3125500

Read more about utility functions at:

https://brainly.com/question/24922430

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