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 concentrated 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 raspberry-cranberry 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. What is its optimal daily production schedule and daily profit?
First, let's determine the per quart cost for both juices.
Cranberry (per quart): $1.20 X 1/4 X 25% = $0.075 concentrate + $0.02 X 75% = $0.015 water + $0.05 container + $0.15 labour = $0.29
Raspberry Cranberry Blend (per quart): $1.20 X 1/4 X 15% + $2.00 X 1/4 X 20% = $0.145 concentrate + $0.02 X 65% = $0.013 water + $0.05 container + $0.18 labour = $0.388
Now we determine the maximum and ...