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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.
Q. How many permutations can you make of the word STATISTICS? Solution: There are 10 letters in the word STATISTICS, i.e. n=10. Three of them are S's, so n 1 =3, three are T'
un prisma retto ha per base un rombo avente una diagonale lunga 24cm. sapendo che la superficie laterale e quella totale misurano rispettivamente 2800cm e3568cm ,calcola la misura
Evaluate the given limit. Solution: In this question none of the earlier examples can help us. There's no factoring or simplifying to accomplish. We can't rationalize &
We will look at three types of progressions called Arithmetic, Geometric and Harmonic Progression. Before we start looking at the intricacies of these let us unders
Bill spent 50% of his savings on school supplies, and then he spent 50% of what was left on lunch. If he had $6 left after lunch, how much did he have in savings at the starting?
Definition 1: Given the function f (x ) then 1. f ( x ) is concave up in an interval I if all tangents to the curve on I are below the graph of f ( x ) . 2. f ( x ) is conca
verify liouville''s theorem for y''''''-y''''-y''+y=0
2/4 + 3/4 =
What is the better buy?a square pizza measuring 8 inches by 8inches that cost $10 or a round pizza with a 9 inch diameter that also cost $10?
how to find area under a curve
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