The SMM Company,which is manufacturing a new instant salad machine, has $350,000 to spend on advertising. The product is only to be test marketed initially in the Dallas area. The money is to be spent on an advertising blitz during one weekend( Friday, Saturday, Sunday) in January and SMM is limited to television advertising.
The company has three options available: day time advertising, everything news advertising and the Super Bowl. Even though the Super Bowl is a national telecast, the Dallas Cowboys will be playing in it and hence, the viewing audience will be epecially large in the Dallas area. A mixture of one minute TV sports is desired. The table below gives pertinent data:

Cost Per Ad Estimated New Audience Reached with Each Ad
Day Time $5000 3000
Evening News $7000 4000
Super Bowl $100,000 75000

SMM has decided to take out at least one ad in each option. Further, there are only two Super Bowl ad spots available. There are 10 day time spots and 6 evening spots available daily. If SMM wants to have at least 5 ads per day, but spend no more than $50,000 on Friday and no more than $75,000 on Saturday, formulate a linear program to help SMM decide how the company should advertise over the weekend.

Solution Preview

OK, first set up the variables. Suppose, we order
x1 Day Time ads on Friday,
x2 Evening Time ads on Friday
x3 Day Time ads on Saturday
x4 Evening Time ads on Saturday
x5 Day Time ads on Sunday
x6 Evening Time ads on Sunday
x7 Super Bowl ads in total

We obviously want to maximize the audience reached. So, let's formulate the ...

Solution Summary

Formulate a linear program to help SMM decide how the company should advertise over the weekend.

What is the profit for the linear program problem below?
MaximizeP = 5X + 10Y
Subject to
X >=2 (Resource A)
3Y <=18 (Resource B)
- 3X + 3Y >=6 (Resource C)
where X , Y >=0
A. Unbounded
B. 50
C. 70
D. 80
F. 85

Consider a symmetric square matrix A and the following linear program:
Min cx
St Ax > c
x > 0
Prove that if x* satisfies Ax* = c and x* > 0 then x* is an optimal solution to this linearprogram.

Is integer values a general property of LinearProgramming problems? Explain why rounding or truncating non-integer values for the solutions is not an appropriate method for obtaining integer solutions.

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

Consider the following linearprogram:
Min 2A+2B
s.t.
1A+3B≤12
3A+1B≥13
1A-1B=3
A,B≥0
a. Show the feasible region.
b. What are the extreme points of the feasible region?
c. Find the optimal solution using the graphical solution procedure.

Given the linearProgram:
Max 3A+4B
s.t.
-1A+2B is less than or equal to 8
1A+2B is less than or equal to 12
2A+1B is less than or equal to 16
A,B is greater than or equal to 0
A. Show the feasible region?
b. Find the optimal solution using the graphical solution procedure?

See attached file.
Please show how you arrived at the solution. Thank you.
Given the linearprogram:
Max 3A + 4B
s.t.
-1A + 2B ≤ 8
1A + 2B ≤ 12
2A + 1B ≤ 16
A, B ≥ 0
a. Write the program in standard form.
b. Solve the problem using the graphical solution procedure.
c. What are the va

1. Finer Furniture produces three types of furniture - tables, chairs, and bookcases. The production of each of these involves both a carpentry process and a finishing process. The time required in each of these as well as lumber requirements in each product are given below:
Table Chair Bookcase Amount available
Lumber

A linearprogram has the objective of maximizing profit = 12X + 8Y. The maximum profit is $8,000. Using a computer we find the upper bound for profit on X is 20 and the lower bound is 9. Discuss the changes to the optimal solution (the values of the variables and the profit) that would occur if the profit on X were increased to