Linear Programming : Echelon or Gauss-Jordan Methods

At rush hours, substantial traffic congestion is encountered at the traffic intersections shown in the
figure. (The streets are one-way, as shown by the arrows.)The city wishes to improve the signals at these corners so as to speed the flow of traffic. The traffic engineers first gather data. As the figure shows, 700 cars per hour come
down M Street to irnerscction A, and 300 cars per hour come down 10th Street to intersection A. A total of x of
these cars leave A on M Street, and x4 cars leave A on 10th Street. The number of cars entering A must equal the number leaving....

An electronics company produces models of stereo speakers, models A, B, and C, and can deliver them by truck van, or station wagon. A tmck holds 2 boxes ofmodel A, 2 ofmodel B, and 3 olmodel C. A van holds 3 boxes of model A, 4 boxes of model B, and 2 boxes of model C. A station wagon holds 3 boxes of model A, 5 boxes of model B, and 1 box of model C.
a. If 25 boxes of model A, 33 boxes of model B. and 22 boxes of model C are to be delivered, how many veh[des of each type should be used so that all operate at hilt capacity?
b. Model C has been discontinued. If 25 boxes of model A and 33 boxes of model B are to be delivered, how many vehicles of each type should be used so that all operate at full capacity?

Researchers have determined that the amount of sugar contained in ice cream helps to determine the overall "degree of like" that a consumer has toward particular flavor. They have also determined that too much or too little sugar will have the same negative affect on the "degree of like" and that this relationship follows a quadratic function. In an experiment conducted at Pennsylvania State University, the following condensed table was obtained.....

Please see the attached file for the fully formatted problems.

1) Using the simplex method, solve the following linearprogramming equation:
Maximize: P= 5x + 2y
Subject to: 4x + 3y <= 30
2x ? 3y <= 6
x>=0 , y>=0
2) Solve the system of linear equation using the Gaus- Jordan elimination method.
a)
3x ? 3y + 4z

A particular diet calls for exactly 1000 units of vitamin A, exactly 1600 units of vitamin C, and exactly 2400 units of vitamin E. An individual is fed a mixture of three foods. Each gram of food 1 contains 2 units of vitamin A, 3 units of vitamin C, and 5 units of vitamin E. Each gram of food 2 contains 4 units of vitamin A, 7

Please answer all the questions and give a detailed explanation for each. (see attached)
1. Use the echelon method to solve the system
2. Use the Gauss-Jordan method to solve the system of equations
3. A cable TV company charges $23 for the basic service plus $5 for each movie
channel. Let C(x) be the total cost in

1. Guassian Elimination is really just using the regular Elimination Method and applying the Triangular Form procedures to a set of linear equations, but without having to write down all the variables in the equations each time. This in itself simplifies the procedure and helps focus on the task. What is the ultimate goal of all

1. Find the sum of the first five terms of the geometric sequence.
A=3, r=2
2
a. 93 b. 5 c. 1 d. 93
2 2
2. Use the Gauss-Jordan method to solve the system of equations.
x - y + 3z = 16
3x + z = 4
x + 2y + z = -4
a. No solution b. (4, 0, -4)

The problem is from Numerical Methods. Please show each step of your solution and tell me the theorems, definitions, etc. if you use any. Thank you.
Start with P0 = 0 and use Jacobi iteration to find.....
(Complete problem found in attachment)