Great Juices makes six types of juiceblends They are A 100 O

Great Juices makes six types of juice-blends. They are A) 100% Orange Juice, B) Orange-Mango-Pineapple, C) Orange Kiwi Strawberry, D) Orange Pineapple, and E) Kiwi Strawberry Mango. The following table lists all the relevant data.

Blends >>>>

A

B

C

D

E

Purchase price $/Gal

Available

Quantity

Gallons

Sold at $/Gal

$2.75

$2.95

$2.80

$3.10

$3.30

Ingredients

Orange J

100%

30%

50%

60%

$1.65

500,000

Kiwi J

20%

40%

$2.00

130,000

Pineapple J

40%

40%

$1.85

100,000

Strawberry J

30%

40%

$2.10

140,000

Mango Juice

30%

20%

$2.40

150,000

Note that you do not have any inventory of the ingredients and everything must be bought.

Other restrictions:

1) Blend A has to be at least 40% of the total production

2) Blend B plus blend C together cannot be more than 20% of the total of other three blends.

3) Blends containing Mango must account for at least 20% of the total.

Formulate a Linear programming model with an objective to maximize profit. Using the names of variables as A, B, C, D, and E, write down the LP in algebraic form as discussed in the class. Neatly write or type the answer in the space provided below.

Solve it and provide the answer: The optimal production quantities of the blends in gallons are.

                 

                  A = _________,                   B = _________,             C =__________,

                  D = _________,                   E = _________.

                  Profit in dollars = $____________________

Blends >>>>	A	B	C	D	E	Purchase price $/Gal	Available Quantity Gallons
Sold at $/Gal	$2.75	$2.95	$2.80	$3.10	$3.30
Ingredients
Orange J	100%	30%	50%	60%		$1.65	500,000
Kiwi J			20%		40%	$2.00	130,000
Pineapple J		40%		40%		$1.85	100,000
Strawberry J			30%		40%	$2.10	140,000
Mango Juice		30%			20%	$2.40	150,000

Solution