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 bourbon. The customer also specified that the blend should be mixed in the ration of two parts rye to one part bourbon. 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 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.

Solve the linear programming model graphically.

Indicate the slack and surplus available at the optimal solution point and explain their meanings.

What increase in the objective function coefficients in this model would change the optimal solution point? Explain the answer.

Solve the linear programming model by using the computer.

Identify the sensitivity ranges for the objective function coefficients and explain what the upper and lower limits are.

How much would it be worth to the distillery company to obtain additional production capacity?

If the customer decided to change the blend requirement for its custom-made whiskey to a mix of three parts rye to one part bourbon, how would this change the optimal solution?