# Eli Orchid has designed a new pharmaceutical product, Orchid Relief, which uses two new ingredients. Eli Orchid can procure limited

## Question:

Eli Orchid has designed a new pharmaceutical product, Orchid Relief, which uses two new ingredients. Eli Orchid can procure limited amounts of each ingredient for each month, that is, the company has 75 tons of ingredient 1 and 60 tons of ingredient 2 available each month.

Eli Orchid can manufacture the new product using any of its three existing processes. The processes are different in their cost per batch of Orchid Relief produced, use different amounts of each ingredient, and yield different amounts of Orchid Relief. Details of the three processes are summarized in the following table.

Process 1 | Process 2 | Process 3 | |
---|---|---|---|

Cost of production per batch | $14,000 | $19,000 | $11,000 |

Ingredient 1 required per batch (tons) | 3 | 2 | 7 |

Ingredient 2 required per batch (tons) | 1 | 7 | 2 |

Orchid Relief yielded per batch (tons) | 2 | 5 | 1 |

Eli Orchid needs to find how many batches to produce with each process. It is interested to do this in the least costly way that produces at least 50 tons of Orchid Relief per month, given the limited availability of the two ingredients.

Verbally state the objective function and all the constraints, define the decision variables and provide a mathematical formulation of the optimization problem. Create an excel spreadsheet that represents your mathematical formulation. Use Excel Solver to find the optimal solution and obtain the sensitivity report. Make sure that you provide proper labeling of objective function, decision variables, and constraints so that the Excel sensitivity report is easier to read.

Then answer the following questions:

1. By how much should the cost of the third process drop so that management is willing to use it to produce Eli Orchid?

2. If the cost of process 2 increased to $36,000 per batch, how much would then be the cost of producing the 50 tons of Orchid Relief?

3. A new maintenance strategy is going to come into place that increases the cost of each of the three processes by $6000. How much would then be the cost of producing the 50 tons of Orchid Relief?

**Related Book For**

## Basic Business Statistics Concepts and Applications

ISBN: 978-0132168380

12th edition

Authors: Mark L. Berenson, David M. Levine, Timothy C. Krehbiel

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