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1. In real world optimisation problems there is often an accompanying constraint that must also be satisfied. These problems are typically solved using "Lagrange Multipliers", which make use of several ideas that you have learned in MAB122.
(a) Consult the library or Internet to investigate how constrained optimisation using Lagrange Multipliers works. Summarise what you find (no more than 1 page).
(b) Use Lagrange Multipliers to determine the point(s) on the surface xy - z2 = 1 which are closest to the origin.
The average U.S. citizen consumes about 2.5 × 102 L of water per day for various uses. In 2013, there were about 3.16 × 108 U.S. citizens. About how many kiloliters of water were c
We've dealt along with this function many times already. Now it's time to graph it. First, let's remember ourselves of the definition of the absolute value function. It is a pie
2x+y/x+3y=-1/7and 7x+36y=47/3 hence find p if xy=p=x/y
Sum of two numbers is 10 and their multipication is 21,find the two numbers. x^2 -10x +21=0
x cubed plus 27??
It is probably the easiest function which we'll ever graph and still it is one of the functions which tend to cause problems for students. The most general form for the constant
x 8/9 + = 6
Now, let's solve out some double inequalities. The procedure here is alike in some ways to solving single inequalities and still very different in other ways. As there are two ineq
If a firm sellings its product at a price $p per unit, customers would buy q units per day where q = 1,350 - p. The cost of producing q units per day is $C(q) where C(q) = 50q + 36
the table shows the number of minutes of excirccise for each person compare and contrast the measures of variation for both weeks
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