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Your task is to design a rectangular industrial warehouse consisting of three separate spaces of equal size. The wall materials cost $71 per linear foot and your company has allocated $34080 for those walls. 1) The dimensions which use all of the budget and maximize total area ar

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thaovtp1407

Answer:

Explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo.

Given:

  • Cost $71 per linear foot
  • Budge $34080 for those walls

Let X is the the length

Let Y is the width

From the photo, we can see that

(4X + 6Y)*71 = 34080

<=> (4X + 6Y) = 480

<=> Y = 80 -  [tex]\frac{2}{3}[/tex]X

The are of the rectangular industrial warehouse:

A(X) = 3Y*X

<=> A(X) = 3(80 -  [tex]\frac{2}{3}[/tex]X )X

<=>A(X) = (240-2X)X = 240X - [tex]2X^{2}[/tex]

So A'(X) = 240 - 4X

Let A'(X) = 0, we have:

240 - 4X = 0

<=> X = 60

=> Y =(80 -  [tex]\frac{2}{3}[/tex]X ) = 80 -  [tex]\frac{2}{3}[/tex]*60 = 40

So the dimension to maximize total area is: 60 in length and 40 in width

Ver imagen thaovtp1407

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