Groovy Juice Mixers, Inc. mixes specialty drinks out of apple, guava, and papaya

Question

Groovy Juice Mixers, Inc. mixes specialty drinks out of apple, guava, and papaya juices. Currently it has 1000, 700, and 400 gallons of each of these kinds of juices in inventory, respectively.


Groovy currently has two products, Tropical Breeze and Guava Jive, which sell for $1.50 and $2.20 per gallon, respectively.


Tropical Breeze is a mixture of all three ingredients that consists of 20% to 25% guava juice, and also 25% to 35% papaya juice.


Guava Jive consists at least 45% and at most 50% guava. It does not have to contain papaya juice, but if it does, it may be at most 15% papaya.


Assume inventory is a sunk cost, and that the costs of mixing are negligible. Therefore, Groovy's goal is to obtain the maximum possible revenue from the inventory on hand.


To do this problem you will need 6 Decision Variables:

TA = Number of Gallons of Apple Juice Used in Tropical Breeze
TG = Number of Gallons of Guava Juice Used in Tropical Breeze
TP = Number of Gallons of Papaya Juice Used in Tropical Breeze

GA = Number of Gallons of Apple Juice Used in Guava Jive
GG = Number of Gallons of Guava Juice Used in Guava Jive
GP = Number of Gallons of Papaya Juice Used in Guava Jive


Find each of the following:
TA =

_______

TG = 196
TP =

_______

GA =

_______

GG =

______

GP = 57

Total Revenue =

____________

(Leave off $ sign and commas)
Hint: Total Revenue is between 3874 and 4014

Explanation / Answer

Solution:

since TG is 196 ,it could be be 20 to 25%..we could use the least value as it is demanded more in guava jive.

196*100/20= 980 gallons of tropical breeze

TP=35% OF 980 = 343 ( LEFTOVER 400-343-57 WILL BE USED IN GUAVA JIVE)

TA=100- (35+20)% OF 980= 45% OF 980=441

GAUVA JIVE

GP=57

57*100/5.1= 1117 GALLONS OF GUAVA JIVE

GG=45% OF 1117=503 GALLONS

GA= 49.9% OF 1117= 557 GALLONS

TOTAL REVENUE= 1.50*980 + 2.20*1117= 3927.40

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