The TMA Company manufactures 19-inch color TV picture tubes in two separate locations: Location I and Location II. The monthly production capacity at Location I is 6000 tubes while that in Location II is 5000.
The picture tubes are shipped in two warehouses: Warehouse A and Warehouse B. Each month 3000 tubes must be shipped to Warehouse A and 4000 tubes to Warehouse B. The shipping costs (in dollars per picture tube) from the TMA plant to the warehouses are tabulated below:

From To Warehouse
A B
Location I $3 $2
Location II $4 $5

Find a shipping schedule that meets the above requirements while keeping the total shipping cost to a minimum. Proceed as follows:

Let x = tubes shipped from Location I to Warehouse A
y = tubes shipped from Location I to Warehouse B

a. Formulate the objective function
b. Formulate the constraints
c. Graph the constraints and indicate the feasible set.
d. Identify the optimal corner point.
e. State the optimal solution to the problem

Please see the attached file for the fully formatted problems.
Please see attached for other Problems.

Two linear programming problems are analyzed with respect to Objective Functions, Constraints, Feasible Area, Slack and Surplus Variables and Optimal Solutions.

1. What are slack, surplus, and artificial variables? When is each used and why?
2. Discuss the similarities and differences between minimization and maximization problems using the graphical solution approaches of linearprogramming.

1. Decision variables
a. tell how much or how many of something to produce, invest, purchase, hire, etc.
b. represent the values of the constraints.
c. measure the objective function.
d. must exist for each constraint.
2. Which of the following is a valid objective function for a linearprogramming problem?
a. Max 5x

Homework problems. File is attached.
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True/False
Indicate whether the sentence or statement is true or false.
______ 1. A linearprogramming model consists of decision variables, constraints, but no objective function.
______ 2. Linearprogramming models exhibit linearity among all constraint relationships and th

PLEASE EXPLAIN YOUR ANSWERS (why did you choose T instead of F or A instead of C, etc.).
C 1. Which of the following is not a component of the structure of a linearprogramming model?
a. parameters
b. decision variables
c. environment of certainty
d. constraints
F 2. In a linearprogramming model, the numb

A. Minimization Graphical Solution
Solve the following linearprogramming model graphically and select the set of extreme points that make up the solution:
Minimize Z = 20X1 + 10X2
subject to:
X1 + X2 < 12
2X1 + 5X2 > 40
X2 < 13
Note: The triplets are in the form of (X1 = ,X2 = , Z = )
a) (0, 12, 120), (0, 8, 80), (2

Enclosed problem in attachment.
a. Graph the constraints for this problem. Use dots to indicate all feasible integer solutions.
b. Solve the LP Relaxation of this problem
c. Find the optimal integer solution.

Solve the following problem graphically.
Max 5X + 6Y
s.t. 17X + 8Y < 136
3X + 4Y < 36
X, Y > 0 and integer
a. Graph the constraints for this problem. Indicate all feasiblesolutions.
b. Find the optimal solution to the LP Relaxation. Round down to find a feasible integer solution. Is this solutio

(See attached file for full problem description)
In the graph area problems looking for the steps
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1. The maximization or minimization of a quantity is the
a. goal of management science.
b. decision for decision analysis.
c. constraint of operations research.
d. objective of linearprogramming.
2. Which of

Consider a feasible solution y to the linear program
Min cx
St Ax = b
x > 0
Let Z = {i | yi = 0}. Show that y is an optimal solution if and only if the following linear program has an optimal objective value of zero:
Min cd
St Ad = 0
di > 0 for all i in Z
Please see the attached file for the fully