Your companym Camel Electronics has developed a new USB memory device that uses a copyrighted, secret silicon compound that you invented. The 640 gigabyte model uses 0.125kg of the compound and the 1 Terabyte model uses 0.4. Over the next production cycle, only 80 kg of the compound are available to the manufacturing division of the company.

Each 640 Gb model uses 10 minutes of manufacturing time, and each 1Tb model uses 12 minutes of manufacturing time. The profit contributions are $10 for each 640 gb model and $15 for each 1Tb model.

Management has specified that 20% of the total production must be the 640 Gb model, 40 hours of manufacturing time are available each week, and the produciton cycle is 2 weeks long. Because of the unusually high demand for the new type of memory stroage device, you can sell all that you make.

1. How many memory devices of each type should be manufactured?

2. What is the maximization formula?

3. List all the constraints

4. Create a diagram visually showing your constraints and the optimal solution.

5. A solution of 80 640 Gb models and 320 1Tb models would satisfy the requirement that 20% of the production run is the 640 GB model. Is this solution workable? If not, why not?

Solution Summary

A Complete, Neat and Step-by-step Solution is provided in the attached file.

In each of parts (a) and (b), an operation * is defined over the set of natural numbers. For each operation, determine these four things.
See Attachment.
Please provide detailed explanation showing all steps and reasoning as well as formal notation for the Proof.
Please post response as a MS Word or PDF file.
Thank

Use Gauss-Jordon method to solve the following system of equations:
2s + y - z =1
x -2y + 2z = 7
3x + y + z =4
I have completed...
2 1 -1 1 1 -2 2 1
1 -2 2 7 R1 <->R2 2 -1 2 7 R1 x 2
3 1 1 4 3 1 1 4 R2 - R1

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

Given the following linear programming problem:
Min Z = 2x + 8y
Subject to (1) 8x + 4y 64
(2) 2x + 4y 32
(3) y 2
At the optimal solution the minimum cost is:
a. $30
b. $40
c. $50
d. $52
d. $53.33

We are studying an inner product spaces. See attached file for full problem description.
Let V be a C-space of all complex valued polynomials with an inner product....
(i) Let p be a polynomial and let Mp: V-> V be a linear operator that is given by
Mp (q) :=p⋅q. Show that operator Mp has an adjoint and find it.
(i

Assume that x2, x7 and x8 are the dollars invested in three different common stocks from New York stock exchange. In order to diversify the investments, the investing company requires that no more than 60% of the dollars invested can be in "stock two". The constraint for this requirement SHOULD be written as:
a) x2 > 0.60

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 the square of the derivative operator D^2
(a) Show that D^2 is a linear operator
(b) Find the eigenfunctions and corresponding eigenvalues of D^2.
(c) Give an example of an eigenfunction of D^2 which is not an eigenfunction of D.

Consider the following network representation of a transportation problem:
The supplies, demands, and transportation costs per unit are shown on the network.
a. Develop a linear programming model for this problem; be sure to define the variables in your model.
b. Solve the linear program to determine the optimal solution.

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