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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.
Memphis, Tennessee, and New Orleans, Louisiana, lie approximately on the same meridian. Memphis has latitude 35°N and New Orleans has latitude 30°N. Find the distance between these
Caterer verifies that 87% of people who sampled the food thought it was delicious. A random sample of 144 out of population of 5000 taken. The 144 are asked to sample the food. If
briefly explain how the famous equation for the loss of heat in a cylindrical pipe is derived
1. If the equation has any fractions employ the least common denominator to apparent the fractions. We will do this through multiplying both sides of the equation by the LCD. Al
Define a complete lattice and give one example. Ans: A lattice (L, ≤) is said to be a complete lattice if, and only if every non-empty subset S of L has a greatest lower bound
1) let R be the triangle with vertices (0,0), (pi, pi) and (pi, -pi). using the change of variables formula u = x-y and v = x+y , compute the double integral (cos(x-y)sin(x+y) dA a
Define A*B where: A = | 3 -3 6 | B = | 6 1 | | 0 4 2 | | 0 -5 |
Marks obtained by 70 students are given below: M arks 20 70 50 60 75 90 40 No.
draw a line OX=10CM and construct an angle xoy = 60. (b)bisect the angle xoy and mark a point A on the bisector so that OA = 7cm
An observation was made concerning reading abilities of males and females. The observation leads to a conclusion that females are faster readers than males. The observation was bas
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