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# How to optimize production

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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?

#### Solution Preview

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 ...

\$2.19

## Linear Programming solve using Graphical Method, Maximization

Formulate each of the following as a Linear Programming Problem. Build the Linear Programming Model and solve using Graphical Method.

1. Wrigley's Company makes two types of chewing gums: Strawberry and Lemon.
The following table shows the profit and the number of hours needed in each department for each type of chewing gum.

Strawberry Lemon Capacity
Mixing department 3 hours 1 hour 300 hours
Molding Department 3 hours 3 hours 540 hours
Cooling Department 4 hours 10 hours 100 hours
Profit 13\$/box 15\$/box

Find out how many of each type of chewing gum should be manufactured in order to maximize the profit.

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