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alisha [4.7K]
3 years ago
9

Maurice has the following utility function: U (X Y) =20X+80Y-X^2-2Y^2, where X is his consumption of CDs with a price of ​$11 an

d Y is his consumption of movie​ videos, with a rental price of ​$2. He plans to spend ​$50 on both forms of entertainment. Determine the number of CDs and video rentals that will maximize​ Maurice's utility.
Business
1 answer:
Schach [20]3 years ago
8 0

Answer:

1 CD and 19 movie videos

Explanation:

This is a quadratic programming problem. Given the utility function, product price and budget constraint. the following relation between X and Y is:

Y =\frac{50-11X}{2}

When that is inserted in the utility function, the function is:

U(X) = -X^{2} -420X+200-\frac{121X^{2}-1100X+2500 }{2}

In order to find the maximization parameter X, the first derivative of the function is needed (leveled with zero), and it is:

-123X + 130 = 0

The value for X is 1,06 which can be rounded to 1. From the first relation, we see that Y is 19.

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What is something I can create or invent that hasn't been invented yet, that could make me a millionaire?
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The total cost​ (in dollars) of manufacturing x auto body frames is ​C(x)=60,000+400x. ​(A) Find the average cost per unit if 20
Nesterboy [21]

Answer:

a) Average price per unit = 700

b) average marginal cost = -1.5 dollars/frame

c) For 201 frames are produced = $698.5

Explanation:

Given Data:

C(x) = 60000 + 400x

a) Average cost for 200 units:

Total Cost of 200 units will be:

C(200) = 60000 + 400(200)

C(200) = 140,000

Total Cost of 200 units = 140,000

Average price per unit = Total Cost / number of units

Average price per unit = 140,000/200

Average price per unit = 700

b) Marginal Average Cost:

We know that marginal cost = C^{'}(x)

And the average marginal cost = \frac{d}{dx} \frac{C(x)}{x}

So,

= the derivative of (\frac{60,000 + 400(x)}{x})

= the derivative of (\frac{(60,000)}{x} + 400)

= \frac{-60,000}{x^{2} } + 0

So,

average marginal cost = \frac{-60,000}{x^{2} }

at x = 200 units

average marginal cost = \frac{-60,000}{200^{2} }

average marginal cost = -1.5 dollars/frame

c) Average cost per frame if 201 frames are produced:

We already seen in the part b that, the average marginal cost is decreasing by 1.5 dollars /frame. So,

if 201 frames are produced the instead of 200 then the difference is of 1 frame and we discussed that average marginal cost of 1 frame is decreasing at 1.5 dollars per frame.

So,

As we know the average cost from part a = 700 dollars.

Therefore, for 201 item = 700 dollars -1.5 dollars

For 201 frames are produced = $698.5

5 0
3 years ago
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