Question

1. Consider the following optimization problem. Find two positive numbers x and y whose sum is 50 and whose product is maximal. Which of the following is the objective function?

A. xy=50

B. f(x,y)=xy

C. x+y=50

D. f(x,y)=x+y

2. Consider the same optimization problem. Find two positive numbers x and y whose sum is 50 and whose product is maximal. Which of the following is the constraint equation?

A. xy=50

B. f(x,y)=xy

C. x+y=50

D. f(x,y)=x+y

3. Consider the same optimization problem. Find two positive numbers x and y whose sum is 50 and whose product is maximal. Solve the problem. What are the optimal values for x and y?

A. x=1, y=49

B. x=20, y=30

C. x=25, y=25

D. x=50, y=50

4. For y=x^2+.5x^3 on the interval -2 <= x <= 1, which of the following is the global maximum?

A. x= 1

B. x= -2

C. x= 0

D. x= .5

Answer #1

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

Find two positive numbers x and y whose sum is 7 so that
x^(2)*y−8x is a maximum.

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

1-Find two positive numbers satisfying the given
requirements.
The product is 238 and the sum is a minimum.
(smaller value) ?
(larger value)?
2-Find the length and width of a rectangle that has the given
perimeter and a maximum area.
Perimeter: 176 meters
length
m
width
m
3-Find the points on the graph of the function that are closest
to the given point.
f(x) = x2, (0, 4)
(x, y)
=
(smaller x-value)
(x, y)
=
(larger x-value)

Find three positive numbers whose sum is 12, and whose sum of
squares is as small as possible, (a) using Lagrange multipliers
b)using critical numbers and the second derivative test.

Let a>0 & b>0 be two positive numbers and consider the
function f(x) = x^a+x^−b. Find the positive value of x where f(x)
achieves its minimum value.
a. x=1
b. x=a/b
c. x=(b/a)^1/a+b
d. x=(ab)^a+b
e. x=(a+b)^ab
f. x=(b/a)^a+b

Suppose you choose two numbers x and y, independently at random
from the interval [0, 1]. Given that their sum lies in the interval
[0, 1], find the probability that (a) |x − y| < 1. (b) xy <
1/2. (c) max{x, y} < 1/2. (d) x 2 + y 2 < 1/4. (e) x >
y

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

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:

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