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.
(b) Solve the problem by using the computer.
(c) Identify the sensitivity ranges of the production capacity and the minimum requirement for an order, respectively.
(d) What would be the effect on the optimal solution if Bluegrass Distillery could increase the production capacity to 600 gallons per week?
(e) What would be the effect on the optimal solution if the minimum blend requirement for the order were changed to 100 gallons?
(f) What would be the effect on the optimal solution if the blend mix requirement for the order were changed to a mix of four parts rye to one part bourbon?