Strayer ACC100 week 8 assignment 1

East Anglia
Tea Company

The East Anglia Tea Company imports three
varieties of tea from Asia: black tea, oolong tea, and green tea. The company
purchases 70 pounds of black tea every week, at a cost of $2.70 per pound.
Also, it purchases 120 pounds of oolong tea at $3.00 per pound, and 150 pounds
of green tea at $2.10 per pound, every week. By mixing these teas in various
combinations, the company creates three tea blends, Mongolian, Manchu, and
House, that it sells to a packaging company for further processing. Mongolian
blend is at least 70% black tea but no more than 10% green tea. Manchu blend is
at least 30% black tea and at least 40% oolong tea. The company’s House blend
is no more than 60% green tea, but its oolong tea component must be at least
30%. The wholesale prices per pound that East Anglia charges the packaging
company are $6.50 for Mongolian blend, $7.25 for Manchu blend, and $6.00 for
House blend.
(a.) How much of each blend should the East Anglia Tea Company make each
week to maximize its profit? Create a linear programming model, and solve it
using the Solver utility of Excel.
(b.)Discuss the sensitivity ranges of the decision variables. Point out
and explain any interesting facts about those ranges.
(c.) Discuss the sensitivity ranges that pertain to the total amounts (of
the three tea varieties) purchased each week. How would variations in those
amounts affect the optimal product mix? What do the shadow prices imply about
the relative values of the three resources (teas)?

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 writeup of the project and the
spreadsheet showing your work.
Writeup.
Your
writeup 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.
Excel.
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.