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