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Sav [38]
2 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]2 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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Statement of stockholders’ equity Financial information related to Organic Products Company for the month ended June 30, 20Y9, i
Nata [24]

Answer:

As for the provided information, we have,

<u>Statement of Stockholder's Equity</u>

Date              Common Stock    Retained Earnings        Total

1 June                $150,000              $1,610,000              $1,760,000

Stock issued       $70,000                                                 $70,000

Net income                                        $112,000                   $112,000

Dividends                                          ($26,000)                 ($26,000)

30 June               $220,000             $1,696,000              $1,916,000

Note: Dividend is deducted from net income.

And net income is a part of retained earnings.

6 0
3 years ago
PLEASE HELP TIME SENSITIVE TEST
Blizzard [7]

Answer:

I think it's services

Explanation:

It best matches the description

8 0
3 years ago
Grandma's Bakery wants to begin selling gluten-free products and vegan products. The C-Suite executives have made the decision a
8_murik_8 [283]

Answer:

The correct answer is letter "B": functional managers.

Explanation:

Functional managers are those in charge of carrying out the operations of a business. These types of executives receive orders from the company's owners -stakeholders- after an analysis of what course the firm should take according to current market conditions so the managers can implement the plan in the organization's activities.

6 0
3 years ago
Your business has purchased 500 pizza pans, 60 kg of sauce, 100 kg of cheese, 2.5 kg of basil, 2.5 kg of oregano, 5 kg of yeast,
adelina 88 [10]

Answer:

400 pizzas

Explanation:

The complete question would be:

<em>You are going into the business of making pizzas. The following is the list of ingredients to make ONE pizza: </em>

<em>400 g flour           50 mL water </em>

<em>10 g yeast             120 g sauce </em>

<em>250 g cheese       5 g oregano </em>

<em>5 g basil </em>

<em>Your business has purchased 500 pizza pans, 60 kg of sauce, 100 kg of cheese, 2.5 kg of basil, 2.5 kg of oregano, 5 kg of yeast, and 200 kg of flour. You have as much water as you need. How many pizzas can you make? </em>

You are going to have to make a couple of conversions to do this. Since everything you need is indicated in grams, we first need to convert everything you have in grams.

There are 1,000 g in 1 kg. So now we convert them all:

60 kg of sauce

60kg \times \dfrac{1,000g}{1kg} = 60,000g

100 kg of cheese

100kg \times \dfrac{1,000g}{1kg} = 100,000g

2.5 kg of basil

2.5kg \times \dfrac{1,000g}{1kg} = 2,500g

2.5 kg of oregano

2.5kg \times \dfrac{1,000g}{1kg} = 2,500g

5 kg of yeast

5kg \times \dfrac{1,000g}{1kg} = 5,000g

200 kg of flour

200kg \times \dfrac{1,000g}{1kg} = 200,000g

So now that we know what we have, we determine how many pizzas we can make with the amount of each ingredient. We get the ratio of each ingredient to one pizza to determine how many we can make:

<u>Flour:</u>

Available: 200,000g

Needed: 400g

200,000g\ of\ flour\times\dfrac{1\ pizza}{400g\ of\ flour} = 500\ pizzas

<u>Yeast:</u>

Available: 5,000g

Needed: 10g

5,000g\ of\ yeast\times\dfrac{1\ pizza}{10g\ of\ yeast} = 500\ pizzas

<u>Cheese:</u>

Available: 100,000g

Needed: 250g

100,000g\ of\ cheese\times\dfrac{1\ pizza}{250g\ of\ cheese} = 400\ pizzas

<u>Basil:</u>

Available: 2,500g

Needed: 5g

<u />2,500g\ of\ basil\times\dfrac{1\ pizza}{5g\ of\ yeast} = 500\ pizzas<u />

<u>Sauce:</u>

Available: 60,000g

Needed: 120g

<u />60,000g\ of\ sauce\times\dfrac{1\ pizza}{120g\ of\ sauce} = 500\ pizzas<u />

<u>Oregano:</u>

Available: 2,500g

Needed: 5g

<u />2,500g\ of\ oregano\times\dfrac{1\ pizza}{5g\ of\ oregano} = 500\ pizzas<u />

We do not need to consider water, because it will provide as many as we will need.

So here we see that all but one ingredient is able to yield 500 pizzas. Cheese is the only one that yields less than 500, specifically 400 only. This is your limiting ingredient and this ingredient determines how many pizzas you can make. Because when you run out of cheese, you can no longer make a pizza.

4 0
3 years ago
Dowd, Elgar, Frost, and Grant formed a general partnership. Their written partnership agreement provided that the profits would
goblinko [34]

Answer:

The answer is: Edgar will receive $37,000

Explanation:

  • Dowd's share of the company's losses is $80,000
  • Edgar's share of the company's losses is $60,000
  • Frost's share of the company's losses is $40,000
  • Grant's share of the company's losses is $20,000

But since Grant is not willing to give more money to the partnership to cover his losses, the $9,000 difference must be divided by the remaining three partners. So they will divide Grant's losses as follows:

  • Dowd's share of the Grant's losses is $3,600
  • Edgar's share of the Grant's losses is $2,700
  • Frost's share of the Grant's losses is $1,800

Then you add up all the losses the three remaining partners had:

  • Dowd' total losses $83,600
  • Edgar's total losses $62,700
  • Frost's total losses $21,800

So when the partnership was dissolved, Edgar should have received $100,000 (capital) - $62,700 (total losses) = $37,200

I selected answer A since they probably rounded down Edgar's share to $37,000 (nearest possible choice).

6 0
3 years ago
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