24. Harry and Melissa Jacobson produce handcrafted furniture in a workshop on their farm. They have obtained a load of 600 board feet of birch from a neighbor and are planning to produce round kitchen tables and ladder-back chairs during the next three months. Each table will require 30 hours of labor, each will require 18 hours, and between them they have a total of 480 hours of labor available. A table requires 40 board feet of wood to make, and a chair requires 15 board feet. A table earns the couple $575 in profit, and a chair earns $120 in profit. Most people who buy a table also want four chairs to go with it, so for every table that produced at least four chairs must also be made, although additional chairs can also be sold separately. Formulate and solve an integer programming model that will determine the number of tables and chairs the Jacobsons should make to maximize profit.

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

With referrence to the last solutions u posted to me,may you please check no 1 I have a different solution from my workings.I not sure which one is correct,but I think mine might be.If so may u please edit the document because I failed to do so.I will use this over and over.

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.

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

Can you help me with the following:
Let ubar and vbar be nonzero vectors in 2 or 3 space and let k=||u|| and m=||v||. Show that the vector Wbar=mubar +kvbar bisects the angle between ubar and vbar.
Please show all steps in detail for my reference.

1. The surface area S of a right prism is given by S = 2B + Ph.
B is the area of the base.
P is the perimeter of the base.
And h is the height of the prism. Solve for B.
2. The length of a rectangle is five times its width. If the area of the rectangle is 500m², find its perimeter.
3. The sum of two numbers is grea

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

Let 0 denote a 2 x 2 matrix, each of whose entries is 0.
a) Is there a 2 x 2 matrix A such that:
A does not equal 0
A*A=0?
b) Is there a 2 x 2 matrix A such that:
A does not equal 0
A*A=A?

Suppose that C [an element of] C^nxn is invertible and the set S = {w_1,...w_k} C [a subset of] C^n is linearly
independent. Prove that CS := {Cw_1,...Cw_k} C [a subset of] C^n is linearly independent.
See the attached file.

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