Calculus help with modeling and optimization.?

Question

These correlate with the extrema/modeling/optimization parts of Calc., which I'm horrible at ): If you can, explain it by showing work. Much appreciated! Someone out there has to know how to do it!

1. An open box of maximum volume is to be made from a square piece of material, 24 inches on a side, by cutting equal squares from the corners and turning up the sides.

a. Write the volume as a function of X.
b. Find the maximum volume of the box.


2. Find two numbers that satisfy the given requirements.

a. The product is 192 and the sum is a minimum.
b. The sum of the first and twice the second is 100 and the product is a maximum.

Answer 1

1.

a.Let X be the length of square cut from the edge.



Volume = (X)(24-X)(24-X)



b. follow the steps

1.differentiate w.r.t X

2. set to zero and determine values of X



2.

a. XY = 192

Y = 192/X



f'(x)

= d (X+Y) / dx

= d(X + 192/X) / dx

= 0



solve for x, if there is more than 2 answer, do a min.max test



b.

X + 2Y = 100

X = 100 - 2Y



f'(Y)

= d(2XY)/dy

= d [2(100-2Y)(Y)] / dy

= 0

Answer 2

Modeling And Optimization Calculus

Answer 3

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RE:

Calculus help with modeling and optimization.?

These correlate with the extrema/modeling/optimization parts of Calc., which I'm horrible at ): If you can, explain it by showing work. Much appreciated! Someone out there has to know how to do it!



1. An open box of maximum volume is to be made from a square piece of material, 24 inches on a...