Math

CalculusQ&A LibraryA rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Material for the base costs $20 per square meter. Material for the sidescosts $12 per square meter. Find the cost of materials for the cheapest such container. (Round your answer to the nearest cent.)$ 519.15Question

Asked Dec 5, 2019

1 views

1 Rating

Step 1

Let L, W & H be the length, width and height.

- L = 2W
- Volume, V = L x W x H = 2W x W x H = 2W
^{2}H = 10 - Hence, W
^{2}H = 5. Hence, H = 5 / W^{2} - Area of the base = L x W = 2W x W = 2W
^{2} - Area of the four sides = 2 x (L x H + W x H) = 2 x (2W x H + W x H) = 6WH
- Material for the base costs $20 per square meter. Material for the sides costs $12 per square meter.
- The cost of materials = C = 20 x 2W
^{2 }+ 12 x 6WH = 40W^{2 }+ 72WH = 40W^{2 }+ 72W x (5 / W^{2}) = 40W^{2 }+ 360 / W

Step 2

In order to minimze the cost,

- its first derivative with resepct to W should be zero.
- And it's double derivative with respect to W should be positive.

Step 3

(Recall the famous rule of differentiation: d(xn) / dx = nxn-1)

dC/dW = 80W - 360 / W2 = 0

Hence, W3&nbs...

Tagged in

Find answers to questions asked by student like you

Show more Q&A

Q: УА C(0, 1 В(1, 1) y vx y=r о х A(1,0 Referring to the figure above, find the volume generated by rot...

A: The region 1 is bounded above the line y = 1 and bounded below by the curve y = x3.To find the volum...

Q: Can you help me solve number 27. Thanks

A: Given,

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. tan(x) 3t ...

A: According to part 1 of the fundamental theorem of calculus,

Q: Use integration by parts to find the integral. (Use C for the constant of integration.)

A: Consider the provided integral,

Q: The root(s) of the function. Enter your answer as a number or string of numbers. Separate multiple a...

A: Given thatf(x) = x – 3x – 2 That is f(x) = -2x – 2 …(1)

Q: Find G'(x) In(8) (4e 6t 1) dt G(x) х G'(x)

A: Given,

Q: evaluate the limit limit as x approaches infinity of x+cos(x)/ x+1

A: To find,

Q: 4) Ashok's investment portfolio changes value at the rate V'(t) 15e0.06 (e0.36 _ 2) where V is in th...

A: Given:

Q: f(x) = x3-8x2+4x+6 Find the Maclauren series for f(x). Then find the exact error if you use the firs...

A: Given, function is