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 percent rye and not more than 250 gallons of rye. The blend cannot contain more than 45% bourbon. The distillery can produce no more than 500 gallons per week, regardless of the blend. The production manager wants to complete the order in one week. The blend is sold for $12 per gallon. The distillery company’s cost per gallon is $4 for rye and $2 for bourbon. The company wants to determine the blend mix that will meet customer requirements and maximize profits.
If a calculated quantity is a fractional amount, leave it as a fractional amount.
a) Formulate the linear programming model for this problem providing the objective function and the constraints and the definition of the variables.
b) Using linear programming, solve the problem for the optimal answer and provide the value of the objective function and the variables at optimality. Provide your linear programming solution.
c) Using the sensitivity analysis output from your solution in b), answer the following two questions:
· Looking at the original problem, suppose the gallons of rye available is now 265 gallons, what is the value of the objective function with the increased availability of rye?
· Looking at the original problem, there has been an improvement in operations and the distillery can now produce up to 600 gallons per week. What is the value of the objective function with the increased production capacity?
d) Now suppose that the company wants to minimize the cost of production. It also wants to ensure that the profit is at least $3,500. Provide the changes to the formulation in part a) that would need to be made for these modifications. You do not need to solve for the optimal answer but only need to changes to the formulation you provided in a).