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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.
An inground pool is pooring with water. The shallow end is 3 ft deep and gradually slopes to the deepest end, which is 10 ft deep. The width of the pool is 30 ft and the length is
det(adj A)for 1*1 matrix
The equation ax2 + 2hxy + by2 =0 represents a pair of straight lines passing through the origin and its angle is tan q = ±2root under h2-ab/(a+b) and even the eqn ax2+2hxy+by2+2gx+
A large pipe dispenses 750 gallons of water in 50 seconds. At this rate, how long will it take to dispense 330 gallons? Find out the number of gallons per second by dividing 75
Jackie invested money in two different accounts, one of that earned 12% interest per year and another that earned 15% interest per year. The amount invested at 15% was 100 more tha
2-3+=3+-4
Suppose a Ferris wheel with radius of 12 meters is rotating at a rate of 2 rotations per minute. a. How fast is a person rising when the person is 3 meters above the horizontal lin
The diagrams drawn to given sets are called as Venn diagrams or Eule -Venn diagrams. Here given the universal set U by points within rectangle and the subset A of the set U given b
Use the definition of the limit to prove the given limit. Solution Let ε> 0 is any number then we have to find a number δ > 0 so that the following will be true. |
1. Write down the canonical equations of the line passing through the point A(2,3, 4) and being parallel to the vector q ={5,0,-1}.
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