Posted: February 9th, 2015

Quantitative Methods

Paper, Order, or Assignment Requirements

East Anglia Tea Company Project Problem

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.

• 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.
• Discuss the sensitivity ranges of the decision variables. Point out and explain any interesting facts about those ranges.
• 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)?

INSTRUCTIONS FOR PROJECT

This project problem has at least three (3) constraints and at least two (2) decision variables. The problem is bounded and feasible, with a single optimum solution (in other words, it won’t have alternate optimal solutions). The problem includes a component that involves sensitivity analysis and the use of the shadow price.

The paper needs to include two (2) deliverables, a short write-up of the project and the spreadsheet showing your work.

Write-up: 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.

Excel: Set up the problem in Excel and find the solution using Solver. Clearly label the cells in the spreadsheet. You will turn in the entire spreadsheet, showing the setup of the model, and the results.