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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.
Solve the fractional equation: Example: Solve the fractional equation 1/(x-2) +1/(x+3) =0 Solution: The LCD is (x - 2)(x + 3); therefore, multiply both sides of t
Iran is trying to decide whether it should pursue its nuclear weapons program, and its decision will be affected in large measure by what it expects the United States to do. Your a
Audrey measured the width of her dining room in inches. It is 150 inches. How many feet huge is her dining room? There are 12 inches in a foot. Divide 150 by 12 to find out the
Thorwarth M., Arisha, A. and Harper P., (2009) Simulation model to investigate flexible workload management for healthcare and servicescape environment, Proceedings of the 2009 Win
what is the muttiplied number of mutttiplacation called
how you know that your first quadrilateral is an isosceles trapezoid
In a parallelogram ABCD AB=20cm and AD=12cm.The bisector of angle A meets DC at E and BC produced at F.Find the length of CF.
Cathy is forming a quilt out of fabric panels that are 6 in through 6 in. She needs to know the total area of her square-shaped quilt. Which formula will she use? The area of a
Find the area of shaded region of circle of radius =7cm, if ∠AOB=70 o , ∠COD=50 o and ∠EOF=60 o . (Ans:77cm 2 ) Ans: Ar( Sector AOB + Sector COD + Sector OEF) = 7
Now we have to start looking at more complicated exponents. In this section we are going to be evaluating rational exponents. i.e. exponents in the form
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