Reference no: EM131068195
Question- Your run a petroleum company that produces motor oil in four plants and ships it to four distributors D1, D2, ..., D4). The details of shipping and producing are on the table below:
|
Plant
|
Production
Capacity (gallons)
|
Production Cost
per gallon
|
Impurities
Level
|
Shipping cost [attributors per gallon
|
|
D1
|
D2
|
D3
|
D4
|
|
Northeast
|
1000
|
$12.40
|
12
|
$ 1.20
|
$ 1.75
|
$ 2.35
|
$ 2.85
|
|
Southeast
|
1250
|
$1135
|
15
|
$ 1.95
|
$ 1.35
|
$ 1.75
|
$ 2.15
|
|
Northwest
|
950
|
$10.85
|
18
|
$ 2.45
|
$ 1.50
|
$ 2.10
|
$ 1.95
|
|
Southwest
|
1200
|
$12.05
|
12
|
$2.75
|
$ 2.25
|
$ 2.00
|
$ 1.45
|
The next table contains the dist 'baton' demand for the motor oil and how their demand can Increase due to advertising. For example, distributor D1 will accept up to 700 gallons of motor oil, plus 0.05 gallons for every dollar you spend on national advertising. Advertising is not separated by distributor: a single expenditure affects all distributors simultaneously. Thus, If you spend $100 on advertising, D1 will accept up to 700 + (0.05)(100) = 705 gallons, D2 will accept up to 600 + (0.1)(100) = 610 gallons, D3 will accept up to 555 gallons, and D4 will accept up to 687.5 gallons.
|
D1
|
D2
|
D3
|
D4
|
|
Base Demand (gallons)
|
700
|
600
|
550
|
675
|
|
Advertising Sensitivity
|
0.05
|
0.1
|
0.05
|
0.125
|
|
Max Impurities level
|
15.0
|
15.0
|
14.0
|
15.5
|
"Max impurities" Indicates the maximum average Impurity level allowed for shipments to each distributor. For Instance, the shipments from the four plants to D1, when mixed together, should have an average impurity level of at most 15.0.
You have at most $59,000 to spend on production, shipping and advertising, and all the distributors pay you $28.50 per gallon. How can you maximize your profits?
a. Draw the network that illustrates the dynamics of this problem.
b. Develop a linear program formulation for this problem (write decision variables, objective function and constraints).
Hint: If needed, you con hove constraints regarding how much you spend. So, the amount you spend shows up both In the objective function (as costs) and in the constraints.
c. Solve the problem using Excel (you can use the Excel file provided that contains all the data).
d. Now, let us study the influence of advertising. How much investing in advertising did increase the total revenue? That is, if the company had not invested in advertising, how much would have been its revenue?
|
Describe the strengths and weaknesses of the research method
: Identify and describe the strengths and weaknesses of the research method used in both research articles in this week's resources. Use a separate copy of the Journal Club Template for Quantitative Research to enter this information for each resear..
|
|
Specify the probability distribution
: You are to take a multiple-choice exam consisting of 100 questions with five possible responses to each. Suppose that you have not studied and so must guess (select one of the five answers in a completely random fashion) on each question. Let r.v...
|
|
Beginning weights and their current weight
: A weight-loss company wants to statistically prove that its methods work. They randomly selected 10 clients who had been on the weight loss program for between 55 and 65 days. They looked at their beginning weights and their current weight. The st..
|
|
How did supervisor contribute to the employee satisfaction
: Summarize an example of a "good boss." How did this supervisor contribute to the employee's satisfaction? Do you think this behavior benefited the organization or just one or a few employees personally?
|
|
Develop a linear program formulation for this problem
: Draw the network that illustrates the dynamics of this problem. Develop a linear program formulation for this problem (write decision variables, objective function and constraints)
|
|
How much current in amps is running through the dishwasher
: When running the dishwasher on electrical power at 120 volts, how much current in amps is running through the dishwasher. Will it cause a 20 amp circuit breaker to break the circuit?
|
|
Increased productivity after allowing their workers
: In Part 1 of your Justification Report assignment, you built up the following sections: Problem Statement, Overview of Alternatives, Criteria, and Methods. In Part 2, you will revise Part 1 based on your instructor's suggestions and add to it the ..
|
|
Example that follows either the binomial
: Give an example that follows either the binomial or Poisson distribution, and why that example follows that particular distribution.
|
|
How does it differ from the gini coefficient for the us
: Identify the tax choice that had the most progressive effect on your overall outcome. Why did it have such a progressive effect? Identify the tax choice that had the most regressive effect on your overall outcome. Why did it have such a regressive ..
|