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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.
Minimum and Maximum Values : Several applications in this chapter will revolve around minimum & maximum values of a function. Whereas we can all visualize the minimum & maximum v
how to explain this strategy? how to do this strategy in solving a problem? can you give some example on how to solve this kind of strategy.
Katie ran 11.1 miles over the last three days. How many miles did she average per day? To ?nd out the average number of miles, you should divide the total number of miles throu
The bowling alley suggests selecting a ball that is 1/7 of the bowlers weight. If the bowler weighs 84 pounds, how much should the bowling ball weigh?
Extended product rule : As a last topic let's note that the product rule can be extended to more than two functions, for instance. ( f g h )′ = f ′ gh + f g ′ h+ f g h′ ( f
Josephine is constructing an open box by cutting the squares off the corners of a sheet of paper sized 20cm by 16cm. She is considering options of 3cm, 4cm and 5cm squares in order
The grade resistance is F=W sin θ, where θ is the grade and W is the weight of the automobile. What is the grade resistance of a 2500 pound car traveling on a 2.6 degree uphill gr
General approach of Exponential Functions : Before getting to this function let's take a much more general approach to things. Let's begin with b = 0 , b ≠ 1. Then an exponential f
If α,β are the zeros of the polynomial 2x 2 - 4x + 5 find the value of a) α 2 + β 2 b) (α - β) 2 . Ans : p (x) = 2 x 2 - 4 x + 5 (Ans: a) -1 , b) -6) α + β =
6 male students and 3 female students sit around a round table. The probability that no 2 female students sit beside each other can be expressed as a/b, where a and b are coprime p
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