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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.
how do you you find 40% if you 35 out of 40
apzza driver delivered 27 pizzas in one night he delivered more then one pizza to only one house . every other hhouse he only delivered pizza to 18 houses . how many pizzas did he
The position of an object at any time t (in hours) is specified by, s (t ) = 2t 3 - 21t 2 + 60t -10 Find out when the object is moving to the right and whiles the object
An elevated cylindrical shaped water tower is in require of paint. If the radius of the tower is 10 ft and the tower is 40 ft tall, what is the net area to be painted? (π = 3.14)
How to calculate costs if you have a computerised payroll package for your large business?
A venn diagram is a pictorial representation of the sample space of an experiment. It is usually drawn as a rectangular figure representing the sample space and it cont
Determine y′′ for x 2 + y 4 = 10 Solution: We know that to get the second derivative we required the first derivative and to get that w
Megan bought x pounds of coffee in which cost $3 per pound and 18 pounds of coffee at $2.50 per pound for the company picnic. Find out the total number of pounds of coffee purchase
1+2+3+78+980
Give the Introduction to Scientific Notation? In mathematics, it can be very difficult and time-consuming to do calculations involving very large and very small numbers. This i
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