# Tagged Questions

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### Lagrange Multipliers to determine min and max

I've got this question in a book of questions I'm doing. Can someone show me step by step how to solve this? Using Lagrange Multipliers for two constraints, determine the maximum and minimum of ...
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### A Lagrange Multiplier Problem : How to deal with this case when $b< 8$

I was trying to solve the following problem of several variables calculus given in my class.I am stuck in a particular case of the problem.Please help me to solve the problem.Thnx in advance. Find ...
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### Right Triangles and Lagrange Multipliers

Suppose that you have a right triangle $a^2+b^2=c^2$ with integral sides. Given a perimeter $p=a+b+c$, how can you use Lagrange multipliers to determine the maximum length of $a$?
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### What do I need to know to understand Lagrange multipliers?

I've seen Lagrange multipliers used as a powerful method for tackling inequalities and some IMO problems, and I'm aware that it's a part of calculus. I'm currently taking BC Calculus in high school, ...
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### Minimize $\sum a_i^2 \sigma^2$ subject to $\sum a_i = 1$

$$\min_{a_i} \sum_{i=1}^{n} {a_i}^2 \sigma^2\text{ such that }\sum_{i=1}^{n}a_i=1$$ and $\sigma^2$ is a scalar. The answer is $a_i=\frac{1}{n}$. I tried Lagrangian method. How can I get that ...
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### HELP please with Optimization with constrain using lagrangian

I am reading this book on optimization and they present the following problem: Lisa wants to maximize her utility U(q1,q2) subject to a budget constrain, budget constrain is $p1*q1+p2*q2=I$. Ok , I ...
A consumer purchases food $X$ and clothing $Y$. Her utility function is given by: $U(X,Y) = XY +10Y$, income is $\$100$the price of food is$\$1$ and the price of clothing is $P_y$. Derive the ...
Use Lagrange multiplier to find absolute maximum and minimum of $f(x,y) =x^2+xy+y^2, x^2+y^2 =8$. What i've done so far.. \$f_x = \lambda g_x \Rightarrow 2x+y =\lambda2x, \\f_y = \lambda g_y ...