MAT540 Assignment Linear Programming Case Study

Question description

Assignment 1. Linear
Programming Case Study
Your instructor will assign a linear programming project for
this assignment according to the following specifications.
It will be a problem with at least three (3) constraints and
at least two (2) decision variables. The problem will be bounded and feasible.
It will also have a single optimum solution (in other words, it won’t have
alternate optimal solutions). The problem will also include a component that
involves sensitivity analysis and the use of the shadow price.
You will be turning in two (2) deliverables, a short
write-up of the project and the spreadsheet showing your work.
Acme Baby foods mixes
two strengths of apple juice. One quart of Beginner’s juice is made from 30
fluid ounces of water and 2 fluid ounces of apple juice concentrate. One quart
of advanced juice is made from 20 fluid ounces of water and 12 fluid ounces of
concentrate. Every day Acme has available 30,000 fluid ounces of water and
3,600 fluid ounces of concentrate. Acme makes a profit of 20¢ on each quart of
Beginner’s juice and 30¢ on each quart of advanced juice. How many quarts of
each should Acme make each day to get the largest profit? How would this change
if Acme made a profit of 40¢ on Beginner’s juice and 20¢ on advanced juice?
Your write-up should introduce your solution to the project
by describing the problem. Correctly identify what type of problem this is. For
example, you should note if the problem is a maximization or minimization
problem, as well as identify the resources that constrain the solution.
Identify each variable and explain the criteria involved in setting up the
model. This should be encapsulated in one (1) or two (2) succinct paragraphs.
After the introductory paragraph, write out the L.P. model
for the problem. Include the objective function and all constraints, including
any non-negativity constraints. Then, you should present the optimal solution,
based on your work in Excel. Explain what the results mean.
Finally, write a paragraph addressing the part of the
problem pertaining to sensitivity analysis and shadow price.
As previously noted, please set up your problem in Excel and
find the solution using Solver. Clearly label the cells in your spreadsheet.
You will turn in the entire spreadsheet, showing the setup of the model, and
the results.
It will be graded on the following:
Thoroughly explained what
type of problem this is and the approach takenObjective function is
specified correctly.All
constraints are correctly specified, including nonnegativity constraints, if
applicableSpecified model is correctly
translated to ExcelCorrect optimum is obtainedThoroughly explained and
correctly answered the sensitivity analysis part of the problemFree of errors in grammar,
spelling, and punctuation.

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