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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
Given the following demand and supply equations determine the market equilibrium price and quantity. QD=30-3p. As=10-5p. Where Q
pochemuha

Answer:

Equilibrium price, p = 2.5

Equilibrium Quantity, Q = 22.5

Explanation:

The equation is:

Qd = 30 - 3p

Qs = 10 + 5p

At equilibrium, Quantity demanded equals quantity supplied

Equate Qd = Qs to find equilibrium price

30 - 3p = 10 + 5p

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Substitute equilibrium price into Qd and Qs equation to find equilibrium Quantity

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2 years ago
Alfarsi Industries uses the net present value method to make investment decisions and requires a 15% annual return on all invest
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Answer:

E. $7,190

Explanation:

Net present value is the present value of after tax cash flows from an investment less the amount invested.

NPV can be calculated using a financial calculator

For project A,

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Cash flow in year 1 = $9,500

Cash flow in year 2 = $9,500

Cash flow in year 3 = $9,500

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NPV = $7190.64

To find the NPV using a financial calacutor:

1. Input the cash flow values by pressing the CF button. After inputting the value, press enter and the arrow facing a downward direction.

2. After inputting all the cash flows, press the NPV button, input the value for I, press enter and the arrow facing a downward direction.

3. Press compute

I hope my answer helps you

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This is the term that is used to refer to the way people reason using their subconscious mind.

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