Problem: 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 300 gallons of the ~ custom blend. The customer specified that the order must contain at least 40% rye and not more than 280 gallons of bourbon. The customer also specified that the blend should be mixed in the ratio of rye to bourbon as 2 to 1 (i.e. rye:bourbon=2:1). The distillery can produce 500 gallons per week, regardless of the blend. The production manager wants to complete the order in 1 week. The blend is sold for $5 per gallon. The distillery company's cost per gallon is $2 for rye and $1.5 for bourbon. The company wants to determine the blend mix that will meet customer requirements and maximize profits.
(a) Formulate a linear programming model for this problem.