According to http://www.whitehouse.gov/omb/budget/fy2006/tables.html, the U.S. government received approximately $2 trillion in funds during the year 2005. Approximately $1.3 trillion had already been promised to programs such as Medicare and Social Security, leaving approximately $700 billion in "discretionary" funds for budget items like defense and education.

Suppose the Department of Defense required at least $440 billion to function and that the total spending by other government departments (Education, Health and Human Services, Food and Drug Administration, Energy, etc.) was required to be at least $480 billion.
Suppose further that every $100 billion spent on defense increased taxpayer satisfaction by 5% while every $100 billion spent on other services increased satisfaction by 3%.

1. Formulate a linear programming problem to maximize taxpayer satisfaction subject to the constraints on discretionary spending.
2. Graph the constraints as when finding the feasible region
3. Can you find a solution that maximizes taxpayer satisfaction? Why or why not?

Solution Summary

The following posting helps with problems involving linear programming, graphing constraints and maximizing taxpayer satisfaction. Neat and step-wise soltuions are provided. A graph is provided as well.

Claims company processes insurance claims, their perm operators can process 16 claims/day and temp process 12/day and the average for the company is at least 450/day. They want to limit claims error to 25 per day total, and the perm generate .5 errors/day and temp generate 1.4 error per day. The perm operators are paid $465/da

The drying time of varnish depends on the amount of certain chemical that s added.
a. Determine a best (least-squares) ft parabola of the form:
T(m) = x1 + x2m + x3m^2 to the data provided n the table below
b) Also, estimate the drying time of the varnish when 3.5 grams of the chemical are added.
Mass (m) of Additive (Gr

Let = c = C is a continuous function .
Let = sup : , for each f in Define T: by
(T ( ))(t) =
for each t , and For each f in .
a) Show that is a bounded linear operator on .
b) Compute , For each n in N, and compute .
c) Suppose that g . Show that the integral equation

Consider a particle described by the Cartesian coordinates (x,y,z) = X and their conjugate momenta (px, py, pz) = p. The classical definition of the orbital angular momentum of such a particle about the origin is L = X x p.
Let us assume that the operators (Lx, Ly, Lz) = L which represent the components of orbital angular mom

Compute the Wronskian of the given set of functions, then determine whether the function is linearly dependent or linearly independent: x^2 - x, x^2 + x, x^2, all x

Are the following examples linear transformations from p3 to p4? If yes, compute the matrix of transformation in the standard basis of P3 {1,x,x^2} and P4 {1,x,x^2,x^3}.
(a) L(p(x))=x^3*p''(x)+x^2p'(x)-x*p(x)
(b) L(p(x))=x^2*p''(x)+p(x)p''(x)
(c) L(p(x))=x^3*p(1)+x*p(0)

Universal Claims Processors processes insurance claims for large national insurance companies. , Most claim processing is done by a large pool of computer operators, some of whom are permanent and some of whom are temporary. A permanent operator can process 16 claims per day, whereas a temporary operator can process 12 per day,

Determine whether the following are linear transformations from C[0,1] into R^1.
L(f) = |f(0)|
L(f) = [f(0) + f(1)]/2
L(f) = {integral from 0 to 1 of [f(x)]^2 dx}^(1/2)
Thanks so much. :)