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vredina [299]
3 years ago
15

A lidless box is to be made using 2m^2 of cardboard find the dimensions of the box that requires the least amount of cardboard

Mathematics
1 answer:
Jlenok [28]3 years ago
5 0
1.8, Problem 37: A lidless cardboard box is to be made with a volume of 4 m3 . Find the dimensions of the box that requires the least amount of cardboard. Solution: If the dimensions of our box are x, y, and z, then we’re seeking to minimize A(x, y, z) = xy + 2xz + 2yz subject to the constraint that xyz = 4. Our first step is to make the first function a function of just 2 variables. From xyz = 4, we see z = 4/xy, and if we substitute this into A(x, y, z), we obtain a new function A(x, y) = xy + 8/y + 8/x. Since we’re optimizing something, we want to calculate the critical points, which occur when Ax = Ay = 0 or either Ax or Ay is undefined. If Ax or Ay is undefined, then x = 0 or y = 0, which means xyz = 4 can’t hold. So, we calculate when Ax = 0 = Ay. Ax = y − 8/x2 = 0 and Ay = x − 8/y2 = 0. From these, we obtain x 2y = 8 = xy2 . This forces x = y = 2, which forces z = 1. Calculating second derivatives and applying the second derivative test, we see that (x, y) = (2, 2) is a local minimum for A(x, y). To show it’s an absolute minimum, first notice that A(x, y) is defined for all choices of x and y that are positive (if x and y are arbitrarily large, you can still make z REALLY small so that xyz = 4 still). Therefore, the domain is NOT a closed and bounded region (it’s neither closed nor bounded), so you can’t apply the Extreme Value Theorem. However, you can salvage something: observe what happens to A(x, y) as x → 0, as y → 0, as x → ∞, and y → ∞. In each of these cases, at least one of the variables must go to ∞, meaning that A(x, y) goes to ∞. Thus, moving away from (2, 2) forces A(x, y) to increase, and so (2, 2) is an absolute minimum for A(x, y).
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dem82 [27]

Answer:

x = 99

Step-by-step explanation:

<u>Step 1:  Solve for x</u>

-12 + x/11 + 12 = -3 + 12

x/11 * 11 = 9 * 11

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A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 5 tables is $39 . The total cost to r
IrinaVladis [17]
3c + 5t = 39....multiply by -3
9c + 7t = 63
----------------
-9c - 15t = - 117 (result of multiplying by -3)
9c + 7t = 63
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t = -54/-8
t = 6.75 <=== tables are 6.75

3c + 5t = 39
3c + 5(6.75) = 39
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3c = 39 - 33.75
3c = 5.25
c = 5.25/3
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Marianne tried to drink a slushy as fast as she could. She drank the slushy at a rate of 4.5 milliliters per second. After 17 se
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Answer:

225 milliliters

Step-by-step explanation:

Marianne tried to drink a slushy as fast as she could. She drank the slushy at a rate of 4.5 milliliters per second. After 17 seconds 148 5 milliliters of slushy remains. how much slushy was originally in the cup?

let x = slushy originally in the cup

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2 years ago
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