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zubka84 [21]
3 years ago
6

A rectangular building with a square front is to be constructed of materials that costs 13 dollars per ft2 for the flat roof, 12

dollars per ft2 for the sides and the back, and 17 dollars per ft2 for the glass front. We will ignore the bottom of the building. If the volume of the building is 5,600 ft3, what dimensions will minimize the cost of materials?
Mathematics
1 answer:
aliina [53]3 years ago
6 0

Answer:

The front side is 11.483 ft while the width of the building is 42.473 ft

Step-by-step explanation:

Volume of the building = 5600 ft³

Area × Width

Side² × Width

Roof dimension = Side × Width

Dimension of side = Side × Width

Dimension of front = Side × Side

Therefore we have, the cost given as follows;

Let the side = S and the width = W

Cost therefore = 13(W·S) +12(2W·S + S²) + 17(S²)

Cost therefore =29·S²+37·W·S

Therefore, we are to minimize 29·S²+37·W·S subject to W·S² = 5600

Which gives

58·S + 37·W = λₓ

37·S =  λ_y

58·S + 37·W = 37·S

37·W = - 21·S

S = -37/21·W

W·S² = 5600

= W·(-37/21·W)² = 5600

W³ = 1803.94

W = 42.473 ft

S = √(5600/42.473)

S = 11.483 ft.

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3 years ago
An animal shelter spends $5.00 per day to care for each bird and $7.50 per day to care for each cat. Jayden noticed that the she
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Answer:

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Step-by-step explanation:

Let b represent the number of birds at the shelter on Wednesday. Then the cost of care for the 41 animals is ...

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The number of birds at the shelter on Wednesday was 24.

7 0
3 years ago
Francis works at Carlos Bakery and is making cookie trays. She has 48 chocolate chip cookies, 64 rainbow cookies, and 120 oatmea
amm1812

The number of cookies and trays are illustrations of greatest common factors.

  • The number of trays is 8
  • 6 chocolate chips, 8 rainbows and 15 oatmeal cookies would fit each tray

The given parameters are:

\mathbf{Chocolate\ chip=48}

\mathbf{Rainbow=64}

\mathbf{Oatmeal=120}

<u>(a) The number of trays</u>

To do this, we simply calculate the greatest common factor of 48, 64 and 120

Factorize the numbers, as follows:

\mathbf{48 = 2 \times 2 \times 2 \times 2 \times 3}

\mathbf{64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2}

\mathbf{120 = 2 \times 2 \times 2 \times 3 \times 5}

So, the GCF is:

\mathbf{GCF= 2 \times 2 \times 2}

\mathbf{GCF= 8}

Hence, the number of tray is 8

<u>(b) The number of each type of cookie</u>

We have

\mathbf{Chocolate\ chip=48}

\mathbf{Rainbow=64}

\mathbf{Oatmeal=120}

Divide each cookie by the number of trays

So, we have:

\mathbf{Chocolate\ chip = \frac{48}{8} = 6}

\mathbf{Rainbow = \frac{64}{8} = 8}

\mathbf{Oatmeal = \frac{150}{8} = 15}

Hence, 6 chocolate chips, 8 rainbows and 15 oatmeal cookies would fit each tray

Read more about greatest common factors at:

brainly.com/question/11221202

4 0
2 years ago
Bridget buys a softball bat during the sale. If the original price was $20, how much does Bridget pay?
rodikova [14]

Answer:

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Step-by-step explanation:

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5 0
3 years ago
Solve the following quadratic equation using the quadratic formula. Which of the following expressions gives the numerators of t
Illusion [34]

I hope the choices for the numerators of the solutions are given.

I am showing the complete work to find the solutions of this equation , it will help you to find an answer of your question based on this solution.

The standard form of a quadratic equation is :

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Hope this helps you!

5 0
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