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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.
During 2008 the average number of beds required per day at St Hallam's hospital was 1800. During the first 50 days of 2008 the average daily requirement for beds was 1830, with a
a + b
Comparison Test Assume that we have two types of series ∑a n and ∑b n with a n , b n ≥ 0 for all n and a n ≤ b n for all n. Then, A. If ∑b n is convergent then t
q5
Example of Trig Substitutions Evaluate the subsequent integral. ∫ √((25x 2 - 4) / x) (dx) Solution In this type of case the substitution u = 25x 2 - 4 will not wo
Before independence, Bangladesh was called Ceylon East Pakistan Bhutan Bangalore Which of the following countries does not have a monarch as head of state? Canada Australia Eire
1. Construct an isosceles triangle whose base is 7cm and altitude 4cm and then construct another similar triangle whose sides are 1/2 times the corresponding sides of the isosceles
Mimi is filling a tennis ball can along with water. She wants to know the volume of the cylinder shaped can. Which formula will she use? The volume of a cylinder is π times the
A compound fraction is a fraction that has other fractions inside its numerator or denominator. Here's an example: While compound fractions can look really hairy, they're r
#questiThe elevation of a telecommunication mast from two points, one due North of the tower and the other South of it are 21.2 degrees and 24.3 degrees respectively, and the two p
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