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Problem 1. Find the maximum and the minimum distance from the origin to the ellipse
x2 + xy + y2 = 3.
Hints: (i) Use x2 + y2 as your objective function; (ii) You can assume that the constraint qualification condition and the second order conditions are satisfied in this problem, as well as in problems 2 and 3.
Problem 2. Maximize f (x, y, z) = yz + xz subject to y2 + z2 = 1 and xz = 3.
Problem 3. (a) Maximize f (x, y) = x2 + y2 subject to 2x + y ≤ 2, x ≥ 0 and y ≥ 0.
(b) Use the Envelope Theorem to estimate the maximal value of the objective function in part
(a) when the first constraint is changed to 2x+ 9/8y ≤ 2, the second constraint is changed to x ≥ 0.1,and the third to y ≥ -0.1.
2. Suppose a file of 35,000 characters is to be sent over a line at 55,000bps. 1. Calculate the overhead in bits and time using asynchronous transmission. Assume 1 start bit
Question 1: What is the minimum number of students each of whom comes from one of the 50 different states, enrolled in a university to guarantee that there are at least 100 who
if 4,a and 16 are in the geometric sequence. Find the value
STATISTICS AND PROBABILITY : Statistics are the only tools by which an opening can be cut through the formidable thicket of difficulties that bars the path of
Find the length of the second diagonal of a rhombus, whose side is 5cm and one of the diagonals is 6cm.
three complain forces of magnitudes 20N 30N and 45N
A solution to a differential equation at an interval α Illustration 1: Show that y(x) = x -3/2 is a solution to 4x 2 y′′ + 12xy′ + 3 y = 0 for x > 0. Solution : We'll
Solve the subsequent proportion: Example: Solve the subsequent proportion for x. Solution: 5:x = 4:15 The product of the extremes is (5)(15) = 75. The produ
1
A small airplane used 5and2over3 gallons of fuel to fly a 2 hour trip.how many gallons were used each hour
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