Angela and Bob Ray keep a large garden in which they grow cabbage, tomatoes, and onions to make two kinds of relish - chow-chow and tomato. The chow-chow is made primarily of cabbage, whereas the tomato relish has more tomatoes than does the chow-chow. Both relishes include onions, and negligible amounts of bell peppers and spices. A jar of chow-chow contains 8 ounces of cabbage, 3 ounces of tomatoes, and 3 ounces of onions, whereas a jar of tomato relish contains 6 ounces of tomatoes, 6 ounces of cabbage, and 2 ounces of onions. The Rays grow 120 pounds of cabbage, 90 pounds of tomatoes, and 45 pounds of onions each summer. The Rays can produce no more that 24 dozen jars of relish. They make $2.25 in profit from a jar of chow-chow and $1.95 in profit from a jar of tomato relish. The Rays want to know how many jars of each kind of relish to produce to generate the most profit.
a. Formulate a linear programming model for this problem.
b. Solve this model graphically.

Solution Summary

The solution provides step by step method for the calculation of optimal solution for a maximization problem using graphical method. Graph of the feasible region is also included.

Convert the following to a maximization problem.
Minimize: w = 2x + 3y + 5z
Subject to: x + y + z ≥ 5
X + y ≥ 7
2x + y + 3z ≥ 6
Do not need to solve. Just answer with the maximization problem.

What are the optimal values of x1, x2, and z?
Consider the following linearprogrammingproblem:
Max Z = $15x + $20y
Subject to : 8x + 5y 40
0.4x + y 4
x, y
Determine the values for x and y that will maximize revenue. Given this optimal revenue, what is the amount of slack associated with the first

Solve the following linear program using the graphical method:
Maximize Z = $9x1 + $15x2
Subject to: 3x2 â‰¤ 18
9x1 + 6x2 â‰¤ 54
x1, x2 â‰¥ 0.
See the attachment.

A. Maximization Graph Solutions
Given the following maximizationlinearprogramming model, which of the possible solutions provided below is NOT feasible?
Maximize Z = 2X1 + 3X2
subject to:
4X1 + 3X2 < 480
3X1 + 6X2 < 600
a) X1 = 120 and X2 =0
b) X1 = 75 and X2 = 90
c) X1 = 90 and X2 = 75
d) X1 = 0 and X2 = 120
Ans

See attach for problem.
The linearprogramming problem. 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

Discuss the requirements of a linearprogramming (LP) model. Provide an example of an LP model and define each variable used. What are the key steps that need to be considered when formulating an LP problem?

39. Max Z = $0.30x + $0.90y
Subject to : 2x + 3.2y <= 160
4x + 2y <= 240
y <= 40
x, y >= 0.
Solve for the quantities of x and y which will maximize Z. What is the value of the slack variable associated with constraint 2?
45. Consider the following transportation problem:
1 2 Supply
1 5 6 100

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).

You are given a linearprogramming problem that has already been solved. The following conditions hold:
(i) You are maximizing the objective function 6x + 5y
(ii) After solving the problem, you found that the optimal solution point occurs at the intersection of exactly two of the constraints, namely constraints: (1) 4x +2y â‰