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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.
of all those survey 390 were under 18 years of age if 20%were 18, how many responded to the survey
2 of 10 =
#a grocer buys a box of 200oranges for $25 he sells them for 15c caluclate his percentage profit
how do you determine and classify all the critical points of a function
A boat tour company charges $11 for a harbour tour and averages 450 passengers on Saturdays. Over the past few months, the company has been experimenting with the price of a tour a
A garden shop wishes to prepare a supply of special fertilizer at a minimal cost by mixing two fertilizers, A and B. The mixture is to contain at least 45 units of phosphate at lea
The Distributive Law : If you were asked to mentally multiply 37 with 9, how would you proceed? 1 would do it as follows - 37 is 30 + 7, 30 x 9 = 270, 7 x 9 = 63, so 270 + 63, th
TYPES OF COMPUTERISED PAYROLL PACKAGES
Let u = sin(x). Then du = cos(x) dx. So you can now antidifferentiate e^u du. This is e^u + C = e^sin(x) + C. Then substitute your range 0 to pi. e^sin (pi)-e^sin(0) =0-0 =0
trigonometric ratios of sum and difference of two angles
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