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Sav [38]
3 years ago
5

The base of an aquarium with given volume V is made of slate and the sides are made of glass. If the slate costs three times as

much (per unit area) as glass, use Lagrange multipliers to find the dimensions of the aquarium that minimize the cost of the materials.
Business
1 answer:
Anit [1.1K]3 years ago
5 0

Answer:

See details on explanation below...

Explanation:

By having  a value for volume (v) the solution is as followed:

Let's develop expression for the cost of materials based on one of the dimensions.

Let w= width of the base;

d= depth of the base; and

h= height of the aquarium

C= cost

C= cost of base + cost of walls

=(5)(w×d)+(1)(2(w+d)×h)

Minimum will be performed when the width and the depth are the same.

So we are only need the case (substituting w for d)

C=5w^2+4wh

Volume in this case is expressed as

v=w^2h

So if we re-write our Cost equation as

C=5w^2+4w^2h/w

So we obtain

C=5w^2+4vw^−1

By finding the minimum cost, we take the derivative of this and set the result to zero.

dC/dw=10w−4vw^−2

So this equation is solved for w and via substitution for d and h.  Once a value has been established for the volume (v)

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3 years ago
7. A legal entity that makes money for reasons other than the owner's profit, where the profits must remain within the
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7 0
3 years ago
On january? 1, 2017, dodge company purchases? $90,000, 7% bonds at a price of 86.4 and a maturity date of january? 1, 2027. dodg
andreev551 [17]

We should note that the bond investment account is recorded at cost by the Bondholder or Investor.

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Therefore, the entry to record should be:

<span>debit Held-to-Maturity Investment in Bonds for $77,760 and credit Cash for $77,760</span>

4 0
4 years ago
Administrative Management Group of answer choices emphasizes perspective of senior managers and that management, as a profession
Vikki [24]

Answer:

The correct answer is the first option: Emphasizes perspective of senior managers and that management, as a profession, can be taught.

Explanation:

To begin with, the term known as "Administrative Management" refers to the discipline whose main purpose is to focus in the efficient and effective organization of people, information and procedures inside the entity that will all lead to the completion of the tasks that are needed to be done in order to achieve the termination of the product or service that organization produces. This particular approach seeks for the employers to achieve the field in where the understand all the contents necessary to analyze what is happening around the organization and be able to work with that as good as possible.

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3 years ago
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Inga [223]

Answer:

33.33%

Explanation:

Given:

Sales revenue = $360,000

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Now,

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or

The gross profit = $360,000  - $240,000  = $120,000

Thus,

the company's gross profit ratio = \frac{\textup{Gross Profit}}{\textup{Sales revenue}}

or

The company's gross profit ratio =  \frac{120,000}{\textup{360,000}

or

The company's gross profit ratio = 33.33%

8 0
3 years ago
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