Question

a) Find two numbers whose sum is a maximum and whose product is 125. What is the maximum sum?

b) Suppose you want the volume of a box to 1,000 ft^3. What should the dimensions of the box be in order to minimize cost given that the box must have a square base?

Answer #1

Find two numbers whose sum is 14 and whose product is the
maximum possible value.
What two numbers yield this product?
______.

1) Find two positive numbers whose sum is 31 and product is
maximum.
2) Find two positive whose product is 192 and the sum is
minimum.

Find two numbers whose sum is 45 and whose product is a maximum.
(If an answer does not exist, enter DNE.)
smaller number:
larger number:

Find two positive numbers whose product is 253 and whose sum is
a minimum.

Find two + numbers x and y whose product xy is 8 and whose sum
is 2x+y is a minimum

Find two non-negative numbers whose sum is 48 and whose product
is a minimum. (If an answer does not exist, enter DNE.)
smaller #:________
larger #:_________

Show work, draw a picture, label your variables. (4pts)
We want to construct a box whose base length is 4 times the base
width. The material used to build the top and bottom cost $10 sq
foot and material used to build the sides cost $6 sq foot. If the
box must have a volume of 60 cubic feet, determine the dimensions
that will minimize the cost to build the box and find the minimum
cost box.
* Give your...

Find the minimum sum of two positive numbers (not necessarily
integers) whose product is 600.
pls circle the answer

A zoo supplier is building a glass-walled terrarium whose
interior volume is to be 205.8 ft cubed .205.8 ft3. Material costs
per square foot are estimated as shown below.
Walls: $5.00
Floor: $3.00
Ceiling: $3.00
A rectangular solid has a base with two sides of length x and y
and a height of length z. The base and the face opposite it are
shaded.
What dimensions of the terrarium will minimize the total cost?
What is the minimum cost?
x...

Find the dimensions and volume of the box of maximum volume that
can be constructed. The rectangular box having a top and a square
base is to be constructed at a cost of $4. If the material for the
bottom costs $0.10 per square foot, the material for the top costs
$0.35 per square foot, and the material for the sides costs $0.25
per square foot,

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