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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.
The Stefan-Boltzmann law can be employed to estimate the rate of radiation of energy H from a surface of copper sphere with radius = 0.15 ±0.01 m, as in H=AesT^4 where H is in watt
Describe the Types of triangles ? Triangles can be classified according to the lengths of the sides or the measures of the angles. 1. Naming triangles by sides An
x+3=2
Consider a class of 55 students. The student names are placed in a hat and 3 names are randomly drawn without replacement. a) If the first person drawn was named the class presi
WHAT IS PRECALC
Vector Function The good way to get an idea of what a vector function is and what its graph act like is to look at an instance. Thus, consider the following vector function.
How to solve big unitary sums?
round to the nearest hundreths 1677.76
Given: ??????? is supp. to ??????? ???? ????? bisects ??????? ???? ????? bisects ??????? Prove: ??????? is a rt. ?
Discuss comparative statics,Market model and Nationa income model
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