Mathematics: Atrash company is designing an open-top, rectangular container that will have a volume of 3645 ft cubed. the cost of making the bottom of the container is $5 per square foot, and the cost of the sides is $4 per square foot. find the dimensions of the container that will minimize total cost.

Atrash company is designing an open-top, rectangular

hebiancao

15.03.2022

L=9.3 ft

b=9.3 ft

h=42.14 ft

Step-by-step explanation:

Given

volume(V)= 3645 ft^3

let L,b,h be length ,breadth and height of cube

Bottom cost (C_1) =5Lb

Side Costs (C_2) =8Lh+8bh

Total cost(C)=5Lb+8Lh+8bh

C= $5\times \frac{3645}{h}+8h\left ( L+b\right )$

considering to be fixed ,cost become the function of L+b

and if h is fixed then Lb is also fixed and for cost to be minimum L+b should be minimum therefore L=b is necessary

thus $b^2=\frac{3645}{h}$

C= $5b^2+\frac{16\times 3645}{b}$

For minimum cost differentiate w.r.t b

$\frac{\mathrm{d}C}{\mathrm{d} b}=10b-\frac{16\times 3645}{b}$

$\frac{\mathrm{d}C}{\mathrm{d} b}=0$

$10b-\frac{16\times 3645}{b}=0$

$b=9.29\approx 9.3 ft$

L=9.3 ft

h=42.14 ft

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lunaandrew332

07.06.2020

3x - y = -16 -> y = 3x + 16

13x - 11y = -12 -> y = 13/11x + 12/11

Step-by-step explanation:

steps provided below

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