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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.
Cylinder The below equation is the common equation of a cylinder. x 2 /a 2 + y 2 /b 2 = 1 This is known as a cylinder whose cross section is an ellipse. If a = b we
A 4-inch by 6-inch photograph is going to be enlarged through increasing each side by the similar amount. The new area is 168 square inches. How many inches is each dimension incre
Use the maximum flow algorithm to find a maximum flow and a minimum cut in the given network, where the capacities of arc CF, EC , DE and BD are w = 13, x = 7, y =1, a
3 3/4+(1 1/49*7/10)
Financial institutions often create synthetic instruments out of existing instruments. In this case an investment bank plans to buy Treasury Bonds with 20-year maturities at their
A vessel in shape of a inverted cone is surmounted by a cylinder has a common radius of 7cm this was filled with liquid till it covered one third the height of the cylinder. If the
1. Find the third and fourth derivatives of the function Y=5x 7 +3x-6-17x -3 2. Find the Tangent to the curve Y= 5x 3 +2x-1 At the point where x = 2.
Integration by Parts -Integration Techniques Let's start off along with this section with a couple of integrals that we should previously be able to do to get us started. Fir
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The King Company is producing two types of products: A and B. Both products are produced on the similar machining operation. The machines operate on two 8-hour shifts, 5 days per w
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