BLENDING
Response to the following problem:
Ocean Juice produces both a cranberry juice cocktail and a raspberry-cranberry blend. Each day Ocean Juice can receive up to 1000 gallons of a raspberry concentrate that costs $2.00 per gallon and up to 4000 gallons of a cranberry concentrate that costs $1.20 per gallon. Purified water, which is in unlimited supply, costs Ocean Juice $0.08 per gallon. The cranberry juice cocktail is 25% cranberry concentrate and 75% water. The raspberry-cranberry blend is 20% raspberry concentrate, 15% cranberry concentrate, and 65% water. The juices are bottled in glass quart containers costing $0.05 each. Other costs including labor and packaging amount to $0.15 per quart for the cranberry juice cocktail and $0.18 per quart for the raspberrycranberry blend. The minimum daily required production is 10,000 quarts of cranberry juice cocktail and 8000 quarts of the raspberry-cranberry blend. The total daily production capacity is 50,000 quarts. Ocean Juice sells the cranberry juice cocktail to stores for $0.75 per quart and the raspberry cranberry blend for $0.95 per quart.
a. What is its optimal daily production schedule and daily profit?
b. How much should Ocean Juice be willing to pay for:
i. An extra quart of production capacity?
ii. Extra gallons of raspberry concentrate?
iii. Extra gallons of cranberry concentrate?