1.
Fixed capital and labor expenses = 1.2million/year
Variable expenses = 2,000/unit of output
Demand: Q = 1000 - 0.1P

A. Calculate profit-maximizing output, price, and profit levels
B. Using the Lagrangian multiplier method, calculate profit maximizing output, price, and profit levels in light of a parts shortage that limits output to 300 this year
C. Calculate and interpret Lagrangian multiplier
D. Calculate the value of having parts shortage eliminated

2.
Employment Budget = 350,000 on tax preparers and accountants
Salary = Accountant: 50,000 and Tax Preparer: 25,000
Q = function of the number of accountants (A) and trained tax preparers (T)
the function of persons assisting in office is given by:
Q = 250A + 100T + 25AT

A. Using the Lagrangian technique, what is the optimal combination of accountants (A) and tax preparers (T), per office, if the objective is to maximize the number of individuals assisted (q)
B. Under the annual budget of 350,000, what is the maximum number of individuals that can be assisted
C. At the optimal use of accountants and tax preparers, how many individuals can be assisted by a $1.00 increase in budget?

3.
Production Function: Q = M + 0.5S + 0.5MS - S^2
M = number of medical staff
S = number of social services
Annual Budget = 1,200,000
Annual Employment Costs = 30,000 for each social service staff and 60,000 for each medical staff

A. Using the Lagrangian technique to determine the optimal combination of social service staff and medical personnel to employ, if the objective is to maximize the number of patients served
B. Under the annual staff budget of 1,200,000, what is the maximum number of patients that can be serviced?
C. At the optimal use of medical and social service staff members, how many extra patiens could be assisted by a $1.00 increase in budget

Solution Summary

This solution is comprised of solution for questions related with Lagrangian Multipliers.

1) Who can explain me Lagrangianmultipliers with drawings scheme etc...
1)I just can't imagine what is happening in space with Lagrangianmultipliers.
2) I did this problem but here also I can't understand it, because I can't understand what is happening in space! could you explain it with drawings and schemes please : the

Fixed capital and labor expenses are $1.2 million per year.
Variable expenses average $2,000 per van conversion.
Q=1,000 - 0.1P where Q is the number of van conversions (output) and P is price.
Calculate the profit maximizing output, price and profit levels.

Considering the surface f(x,y)=xy and the constraint x2+y2=1 , answer to the following questions:
A. Using the Lagrange multipliers method we can obtain some possible maximum and minimum for ?=ï?±1/2
B. The Lagrange multipliers method is the most convenient
C. There are two absolute maximum and two absolute minimum
D. Th

A system with one degree of freedom has a Hamiltonian
see attached
where A and B are certain functions of the coordinate q and p is the momentum conjugate to q.
a) Find the velocity q(dot)
b) Find the Lagrangian L(q q(dot)) (note variables)

Problem:
A) Write the Lagrangian for a simple pendulum consisting of a mass m suspended at the end of a massless string of length l. Derive the equation of motion from the Euler-Lagrange equation, and solve for the motion in the small angle approximation.
B) Assume the massless string can stretch with a restoring force F=-k(r

With reference to Figure 2, a small cylinder sits initially on top of a large cylinder of radius a, the latter being attached rigidly to a table. The smaller cylinder has mass m and radius b. A small perturbation sets the small cylinder in motion, causing it to roll down the side of the large cylinder. Assume that the coefficien

Please see the attached file.
I need an explanation of how one gets from the top equation (with v)s given by to the bottom equation where v is given by l*(theta)dot. I do not need an explanation of the double pendulum.
Derive the kinetic energy equation of the double pendulum in Lagrangian.

Consider the problems of maximizing u(x) subject to px = y and maximizing v(u(x)) subject to px = y, where v(u) is strictly increasing over the range of u. Prove that x* solves the first problem if and only if it also solves the second problem.
This is what I got, however i dont think its entirely correct.
To solve the