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:

9. Up to how much should Eli Orchid be willing to pay more to obtain an amount of 10 more tons of ingredient 1? (Find the answer using sensitivity report only):

10. The management thinks that the pharmaceutical market is going to improve over the next month so that it can sell 5% more Orchid Relief and at the same time procure 3% more of ingredient 2. However, thinking that they might have too much ingredient 1, the plan is to cut on some of the ingredient 1 and reduce its supply by 5%. How much more does it cost to produce the higher required amount of Orchid Relief? (Find the answer using sensitivity report only):