7. 3/9 points | Previous Answers WaneFM6 4.3.054 My Notes Ask Your Teacher The A

Question

7. 3/9 points | Previous Answers WaneFM6 4.3.054 My Notes Ask Your Teacher The Arctic Juice Company makes three juice blends: PineOrange, using 2 quarts of pineapple juice and 2 quarts of orange juice per gallon; PineKiwi, using 3 quarts of pineapple juice and 1 quart of kiwi juice per gallon; and OrangeKiwi, using 3 quarts of orange juice and 1 quart of kiwi juice per gallon. The amount of each kind of juice the company has on hand varies from day to day. How many gallons of each blend can it make on a day with the following stocks? (Use matrix inverses to find the solutions.) (a) 910 quarts of pineapple juice, 790 quarts of orange juice, 420 quarts of kiwi juice PineOrange PineKiwi OrangeKiwi gal gal gal (b) 560 quarts of pineapple juice, 830 quarts of orange juice, 330 quarts of kiwi juice PineOrange PineKiwi OrangeKiwi gal gal gal (c) A quarts of pineapple juice, B quarts of orange juice, C quarts of kiwi juice PineOrange4 OrangeKiwi

Explanation / Answer

a) Let pineapple juice = x

Let orange juice = y

Let kiwi juice = z

So,

2x + 3y = 910

2x + 3z = 790

Subtract above two eq:

3y - 3z = 120

y - z = 40

y + z = 420

add these above two eq:

2y = 480

y = 240, z = 180

and x = 95

So, pineorange made = 110 gal

Pine KIWI = 230 gal

Orange Kiwi = 190 gal

b)

Let pineapple juice = x

Let orange juice = y

Let kiwi juice = z

So,

2x + 3y = 560

2x + 3z = 830

Subtract above two eq:

3z - 3y = 270

z - y = 90

y + z = 330

add these above two eq:

2z = 420

z = 210, y = 120

and x = 100

So, pineorange made = 100 gal

Pine KIWI = 120 gal

Orange Kiwi = 210 gal

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