Blog

A company makes four juice products using apple, grape, and…

A company makes four juice products using apple, grape, and cranberry juice. Cranberry juice sells for $2.00 per quart, grape juice sells for $2.20 per quart, cranberry-apple juice (a blend of cranberry and apple juice) sells for $2.40 per quart, cranberry-grape juice (a blend of cranberry and grape juice) sells for $2.60 per quart. Each product is produced in a one-quart size (there are four quarts in a gallon). On hand are 400 gallons of apple juice, 600 gallons of grape juice, and 800 gallons of cranberry juice. The cost per gallon is $1.60 for apple juice, $2.00 for grape juice, and $1.80 for cranberry juice. Cranberry juice must comprise at least 50% of the cranberry-apple juice product. Cranberry juice must comprise at least 40% of the cranberry-grape juice product. Cranberry juice may comprise no more than 60% of the cranberry-apple juice product. Cranberry juice may comprise no more than 60% of the cranberry-grape juice product. Cranberry-apple juice containers may comprise no more than 25% of the number of containers produced. The ratio of quart containers of cranberry-apple juice to cranberry-grape juice must be at least 7 to 5. Formulate a linear programming model that will determine the number of containers of each product to produce so as to maximize profit. [When developing your formulation, do not attempt to solve or partially-solve the problem in any way].