# Formulate a Linear Program for Blend Mix at Bluegrass Distillery

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 bourbom. The customer also specified that the blend should be mixed in the ratio of two parts of 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. Formulate a linear programming model for this problem.

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#### Solution Preview

Let x = amount of rye whiskey

Let y = amount of bourbon whiskey

The question states that the customer specified that the order must contain at least 40% of rye, which gives a constraint of

x >= (0.40)(400)

x >= 160

and not more than 250 gallons of bourbon, which gives a constraint of

y <= 250

The customer also specified that the blend should be mixed in the ratio of two parts of bourbon to one part of rye. Thus, this gives the constraint of

x + 2y >=400

The distillery can produce 500 gallons in one week, regardless of the blend. Thus, this gives the constraint of

x + y <=500

Since the blend is sold for $5 per gallon, and costs $2 for rye and $1 for bourbon, the objective function is

Z = Amount sold - Cost

If you want to maximize profit.

Thus, the objective function ...

#### Solution Summary

Solution contains a detailed description for developing a linear program. 830 words.