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.