# Linear programming

The Bluegrass Distillery produces custom blended whiskey. A particular blend consists of rye and bourbon whiskey. The company has received an order for a minimum of 400 gallons of the custom blend. The customer specified that the order must contain at least 40% rye and not more than 250 gallons of bourbon. The customer also specified that the blend should be mixed in the ratio of two parts rye to one part bourbon. The distillery can produce 500 gallons per week regardless of the blend. The production manager wants to complete the order in one week. The blend is sold for $5 per gallon.

The distillery company's cost per gallon is $2 for rye and $1 for bourbon. The company wants to determine the blend mix that will meet customer requirements and maximize profits.

On the computer, formulate a linear programming model for this problem using excel solver.

A) Identify the sensitivity ranges for the objective function coefficient and explain what the upper and middle limits are.

B) How much would it be worth to the distillery to obtain additional production capacity?

C) if the customer decided to change the blend requirements for its custom-made whiskey to a mix of three parts rye to one part bourbon, how would this change the optimal solution?

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#### Solution Summary

Solution to Linear programming are provided in details.