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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.
On 30 June 2012 Bill purchase a home by taking out a 30 year mortgage of $600,000 at 6% interest per annum, compounded months. Repayments are made at the end of each month. (a) Cal
Evaluate distance traveled by train: A plane flying at 525 miles per hour completes a trip in 2 hours less than another plane flying at 350 miles per hour. What is the distan
Sketch the graphs of the following functions: (A) y = 1/(x 2 +1) (b) x= sin x,
Carmen bought 3 pounds of bananas for $1.08. June paid for her purchase of bananas. If they paid the same price per pound, how many pounds did June buy?
What percent of the figure below is shaded? Break the rectangle into eighths as shown below. The shaded part is 6/8 or 3/4 ; 3/4 is 75%.
A medical survey was conducted in order to establish the proportion of the population which was infected along with cancer. The results indicated that 40 percent of the population
x>4
Oscar sold 2 glasses of milk for each 5 sodas he sold. If he sold 10 glasses of milk, how many sodas did he sell? Set up a proportion along with milk/soda = 2/5 = 10x. Cross mu
Q. Show Inverse Trigonometric Functions? Ans. Many functions, including trig functions, are invertible. The inverse of trig functions are called ‘inverse trig functions'.
Q. Define Number Line? Ans. A number line is a nice way to visualize and examine the ordering of the positive and negative numbers. Every positive and negative number that
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