Mathematics, 23.10.2019 01:00 Fetty1738

Refer to the data. if the consumer has money income of $52 and the prices of j and k are $8 and $4 respectively, the consumer will maximize her utility by purchasing:
a. 2 units of j and 7 units of k.
b. 5 units of j and 5 units of k.
c. 4 units of j and 5 units of k.
d. 6 units of j and 3 units of k.

Answers: 2

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Answers

Answer from: crystalrc3414

Option C ( 4 units of J and 5 units of K)

Step-by-step explanation:

First of all to maximize utility means to get the most value from the available money, and in this case it means to buy the maximum amount of items J and K with 52 dollars.

Option C is for 4 units of J and 5 units of K 1 unit of J costs 8 dollars, therefore 4 units of J would cost 4×8=32 dollars. 1 unit of K costs 4 dollars, therefore 5 units of J would cost 5×4= 20 dollars. The total cost of 4 units of J and 5 units of K would be equal to 32+20= 52 dollars. From the calculations above we are able to but 4 units of J and 5 units of K with the 52 dollars and without having and change left or being in debt. This would mean we have maximized our utility. If we were to buy 2 units of J and 7 units of K as I option A, we would have a total of 44 dollars which leaves us with a change of 8 dollars. We could still have bought one more of item J or 2 more of item K with the change. Therefore we would not have maximized our utility (the money) if we had done chosen A. The same applies if we go with options B and D, but in this case we would be spending more than what we have.

Answer from: widnickab

The correct answer is c. 4 units of J and 5 units of K.

Step-by-step explanation:

To maximize the utility income we have to try to use most of the $52 buying J and K.

The equation is Utility= J *$8 + K * $4

a. 2 units of J and 7 units of K.

Utility= 2 *$8 + 7 * $4= 44 We have more money to spend.

b. 5 units of J and 5 units of K.

Utility= 5 *$8 + 5 * $4= 60 We don´t have enough money.

c. 4 units of J and 5 units of K.

Utility= 4 *$8 + 5 * $4= 52 maximize.

d. 6 units of J and 3 units of K.

Utility= 6 *$8 + 3 * $4= 60 We don´t have enough money.

Answer from: Quest

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,

b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,

and solve for the variable

* lets solve the problem

∵ $7^{x}=77$

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴ $ln(7^{x})=ln(77)$

- use the rule $ln(a^{n})= nln(a)$

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴ $x=\frac{ln(77)}{ln(7)}=2.23$

* the solution of the equation is 2.23 to the nearest 2 decimal places

Answer from: Quest

a. geometricb. g[h] = (3/4)·g[h-1]; g[1] = 384c. g[h] = 384·(3/4)^(h-1)d. g[12] ≈ 16.2183 gallonse. g[12] ≈ 64.8732 quarts

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt