Explore BrainMass
Share

Formulate a Linear Program for Blend Mix at Bluegrass Distillery

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

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.

© BrainMass Inc. brainmass.com October 24, 2018, 5:49 pm ad1c9bdddf
https://brainmass.com/engineering/structural-engineering/formulate-a-linear-program-for-blend-mix-at-bluegrass-distillery-22016

Solution Preview

Let x = amount of rye whiskey
Let y = amount of bourbon whiskey

The question states that the customer specified that the order must contain at least 40% of rye, which gives a constraint of

x >= (0.40)(400)
x >= 160

and not more than 250 gallons of bourbon, which gives a constraint of

y <= 250

The customer also specified that the blend should be mixed in the ratio of two parts of bourbon to one part of rye. Thus, this gives the constraint of

x + 2y >=400

The distillery can produce 500 gallons in one week, regardless of the blend. Thus, this gives the constraint of

x + y <=500

Since the blend is sold for $5 per gallon, and costs $2 for rye and $1 for bourbon, the objective function is

Z = Amount sold - Cost

If you want to maximize profit.

Thus, the objective function ...

Solution Summary

Solution contains a detailed description for developing a linear program. 830 words.

$2.19
See Also This Related BrainMass Solution

Linear programming model on excel is assessed.

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 ratio 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 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.

On the computer, formulate a linear programming model for this problem using excel solver.

A) Identify the sensitivity ranges for the objective function coefficient and explain what the upper and middle limits are.

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

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

View Full Posting Details