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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.
for all real numbers x, x 0
find s10 for the arithmetic sequenxe inwhich a1=5 and a10=68
i dont understand angels and lines
Ut=Uxx+A exp(-bx) u(x,0)=A/b^2(1-exp(-bx)) u(0,t)=0 u(1,t)=-A/b^2 exp(-b)
The revenue and cost functions for producing and selling quantity x for a certain production facility are given below. R(x) = 16x - x 2 C(x) = 20 + 4x a) Determine the p
Doing the following exercise will give you and opportunity to think about this aspect of children. E1) List some illustrations of exploration by four or five-year-olds that you
Multiply and divide by root2, then root2/root2(sinx+cosx) = root2(sinx/root2 + cosx/root2) = root2(sinx cos45+cosx sin45) = root2(sin(x+45))
Integrate following. ∫ -2 2 4x 4 - x 2 + 1dx Solution In this case the integrand is even & the interval is accurate so, ∫ -2 2 4x 4 - x 2 + 1dx = 2∫ o
Use the graph of y = x2 - 6x to answer the following: a) Without solving the equation (or factoring), determine the solutions to the equation x 2 - 6x = 0 usi
3^2=8
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