Part I: Identifying Constraints
Each short scenario describes a business situation. For each scenario, please write a short paragraph explaining which constraint or constraints is/are present, and why.
Part II: Describing Constraints
For each situation, write down the appropriate constraint. Please use the standard symbols “+” and “-” for plus and minus, and “ * ” for multiplication; however, if you find the symbols “≤” and “≥” difficult to keep straight, you may write “LE” for “Less than or equal to,” and “GE” for “Greater than or equal to.”
Example: An office is buying filing cabinets. The Model A cabinet holds a maximum of 3 cubic feet of files. Model B holds a maximum of 4.5 cubic feet of files. At any time, the office will have a maximum of 17 cubic feet of files that need to be stored. (A bit more cabinet space wouldn’t be a problem, but not enough would be. The files can’t be stacked on the floor.) Write a constraint on the number of cabinets the office should acquire.
A = number of Model A cabinets purchased
B = number of Model B cabinets purchased
A*( 3 cubic feet) + B*(4.5 cubic feet) ≥ 17 cubic feet
A*( 3 cubic feet) + B*(4.5 cubic feet) GE 17 cubic feet
C = number of cups made
B = number of bowls made
V = number of vases made
GenA = number of type A generators shipped
GenB= number of type B generators shipped
3. Patty (see 2.1. above) earns the following profit on each product:
Using the variable labels given in 2.1, write the profit equation for one of Patty’s days.
Part III: Solving an Allocation Problem
A small Excel application, LP Estimation.xlsx is available to help you with this part of the Case.
A refinery produces gasoline and fuel oil under the following constraints.
gas = number of gallons of gasoline produced per day
fuel = number of gallons of fuel oil produced per day
Minimum daily demand for fuel oil = 3 million gallons (fuel ≥ 3)
Maximum daily demand for gasoline = 6.4 million gallons (gas ≤ 6.4)
Refining one gallon of fuel oil produces at least 0.5 gallons of gasoline.
(fuel ≤ 0.5*gas; gas ≥ 2 fuel
Wholesale prices (earned by the refinery):
Gas: $1.90 per gallon
Fuel oil: $1.5 per gallon.
Your job is to maximize the refinery’s daily profit by determining the optimum mix of fuel oil and gasoline that should be produced. The correct answer consists of a number for fuel oil, and a number for gasoline, that maximizes the following profit equation:
P = (1.90)*gas + (1.5)*fuel (Answer will be in millions of dollars.)
Run at least 10 trials, and enter the data into a table that should look something like this:
|Trial production values:||Profit:|
Here’s how the “LP Estimation” worksheet is set up:
The tentative production goals are between the allowable minimum and maximum for each. Note that the maximum fuel oil that can be produced depends upon the gas production. Conversely, the minimum gas that can be produced depends upon the fuel oil production. If you don’t use the worksheet, the challenge will be to find test values for both oil and gas production that jointly satisfy the constraints.
Note: This is NOT how such a problem is usually solved. Rather, it is solved using LP. The purpose of this exercise is to acquaint you with the type of problem that’s usually solved using LP, and give you an appreciation of how difficult such a problem would be without LP.
We value our customers and so we ensure that what we do is 100% original..
With us you are guaranteed of quality work done by our qualified experts.Your information and everything that you do with us is kept completely confidential.
You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.Read more
The Product ordered is guaranteed to be original. Orders are checked by the most advanced anti-plagiarism software in the market to assure that the Product is 100% original. The Company has a zero tolerance policy for plagiarism.Read more
The Free Revision policy is a courtesy service that the Company provides to help ensure Customer’s total satisfaction with the completed Order. To receive free revision the Company requires that the Customer provide the request within fourteen (14) days from the first completion date and within a period of thirty (30) days for dissertations.Read more
The Company is committed to protect the privacy of the Customer and it will never resell or share any of Customer’s personal information, including credit card data, with any third party. All the online transactions are processed through the secure and reliable online payment systems.Read more
By placing an order with us, you agree to the service we provide. We will endear to do all that it takes to deliver a comprehensive paper as per your requirements. We also count on your cooperation to ensure that we deliver on this mandate.Read more