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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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Answer:

C) formed a valid contract because Rachel's outward expressions showed the formation of a contract.

Explanation:

A valid contract is a binding and enforceable agreement, where all parties are legally bound to perform the contract.

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In this case, Rachel accepted Julius´s offer to buy her boat, so an offer and acceptance exists.

6 0
3 years ago
The trading principle formulated by adam smith maintained that:
erma4kov [3.2K]
The correct answer is D. Absolute cost differences regulate the immediate basis for trade
Absolute gain is the ability of a country, separate, company or region to make a good or service at a lower cost per unit than the cost at which any other individual produces that same good or service.
6 0
3 years ago
Nielson Motors sold 10 million shares of stock in an SEO. The market price of Nielson's stock at the time was $37.50. Of the 10
Yuliya22 [10]

Answer:

a. $144 million

Explanation:

The computation of the amount of money raised is shown below:

But before that we have to find out the amount raised and underwriting fees which is given below:

Amount raised by company is

= 4 million × $37.5  

= $150 million

And,

underwriting fees is

= $150 million × 4%

= $6 million

So, amount raised by the company is

= $150 million - $6 million

= $144 million

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5 0
3 years ago
A _____ is targeted to borrowers with low credit scores, high debt-to-income ratios, or other signs of a reduced ability to repa
Andrej [43]
It would be <span>Subprime mortgage loan.
Hope this helps! :D</span>
3 0
3 years ago
Smart Stream Inc. uses the total cost method of applying the cost-plus approach to product pricing. The costs of producing and s
Amiraneli [1.4K]

Answer:

(a). Total variable Cost = $2,890,000

Total variable Cost Per Unit  = $289  

(b). Variable Cost Markup Percentage = 12.46%

(c). Selling Price Per Unit = $325

Explanation:

According to the scenario, computation of the given data are as follow:-

a). Total Fixed Cost = Selling and Administrative Expenses + Factory Overhead

= $140,000 + $350,000 = $490,000

Fixed Cost Per Unit = Total Fixed Cost ÷ Cost of Produced and Selling Units

= $490,000 ÷ 10,000 = $49

Total variable Cost Per Unit = Fixed Cost Per Unit + Variable Cost Per Unit

= $49 + $240 = $289

Total variable Cost = Cost of Produced and Selling Units × Total Cost Per Unit

= 10,000 × $289 = $2,890,000

b). Desired Profit = Invested Assets × 30%

= $1,200,000 × 30÷100 = $360,000

Variable Cost Markup Percentage = Desired Profit ÷ Total Cost

=$360,000 ÷ $2,890,000 = 0.1246 = 12.46%

c). Selling Price Per Unit = (1 + Variable Cost Markup Percentage) × Total Cost Per Unit

= (1 + 12.46%) × $289

= 1.1246 × $289

= $325

7 0
3 years ago
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