The Arctic Juice Company makes three different kinds of juic

The Arctic Juice Company makes three different kinds of juice blends: PineOrange, PincKiwi, and OrangeKiwi. Each barrel of PineOrange requires 2 quarts of pineapple juice and 2 quarts of orange juice. Each barrel of PincKiwi requires 3 quarts of pineapple juice and 1 quart, of kiwi juice. Each barrel of OrangeKiwi requires 3 quarts of orange juice and 1 quart of kiwi juice. Today the company has 800 quarts of pineapple juice, 650 quarts of orange juice, and 350 quarts of kiwi juice available. How many barrels of each juice blend should they make today if they want to use up all the supplies?

Solution

Let x barrels of Pine orange

Let y barrels of Pine kiwi

Let z barrels of Orange kiwi

Pine orange :pineapple 2x , orange juice 2x

Pine kiwi : 3y pineapple juice , y kiwi juice

Orange kiwi : orange juice 3z , z kiwi juice

Total 800 quarts of pineapple juice: 800 = 2x +3y ----(1)

650 = 2x +3z ----(2)

350 = y +z ---- (3)

Solve the above equations : x = 100 (barrels of pine orange) ; y = 200 (Pine kiwi ) ; z = 150 (Orange kiwi)