The stock brokerage firm of Blank, Leibowitz, and Weinberger has analyzed and recommended two stocks to an investors' club of college professors. The professors were interested in factors such as short-term growth, intermediate growth, and dividend rates. These data on each stock are as follows:

Stock $
Factor Lousiana Gas & Power Trimex Insulation Co.
Short-term growth potential per $ invested 0.36 0.24

Intermediate growth potential (over next 3 yrs), per $ invested 1.67 1.5

Dividend Rate Potential 4% 8%

Each member of the club has an investment goal of (1) an appreciation of no less than $720 in the short term, (2) an appreciation of at least $5,000 in the next three years, and (3) a dividend income of at least $200 per year. What is the smallest investment that a professor can make to meet these three goals?

1. Solve the linearprogrammingproblem:
minimize z = x + y
subject to
x + 2y =< 40,
2x + y =<40,
x + y =<10,
x >= 0, y >=0
The corner points are: (0, 10), (0, 20), (40/3, 40/3) (20, 0), (10, 0).

Which of the following could be a linearprogramming objective function?
Z = 1A + 2B / C + 3D
Z = 1A + 2BC + 3D
Z = 1A + 2B + 3C + 4D
Z = 1A + 2B2 + 3D
all of the above.

Given the following linearprogrammingproblem:
Min Z = 2x + 8y
Subject to (1) 8x + 4y is greater than or equal to 64
(2) 2x + 4y is greater than or equal to 32
(3) y is greater than or equal to 2
What is the minimal solution?

See attach for problem.
The linearprogrammingproblem. Minimize 5x - y subject to:
-2x - 2y < 12
-3x + 2y > 0
x > 0, y > 0
is equivalent to the linearprogrammingproblem:
a. Maximize 5x - y subject to:
-2x -2y < 12
3x - 2y < 0
x > 0, y > 0
b. Maximize 5x-y subject to:
-2x -2y

Consider the following linearprogrammingproblem
MIN Z = 10x1 + 20x2
Subject to: x1 + x2 12
2x1 + 5x2 40
x2 13
x1 , x2 0
What are the values of x1 and x2 at the extreme points of the feasible region ?

State the dual of the following linearprogrammingproblem.
Minimize w = 5y_1 + 8y_2
Subject to: 2y_1 5y_2 ≥ 9
2y_1 + 3y_2 ≥ 11
7y_1 + 2y_2 ≥ 5
With y_1 ≥ o, y_2 ≥ 0.
Please see attachment for better format.

Linearprogramming
Items X1 X2
Profit per Item 3 6
Resource constraints Available Usage Left over
1 7 3 40 0 40
Output
X1= 0
X2= 0
Z= 0
Solve the following linearprogramming model by using the computer
Minimi