The Arctic Juice Company makes three juice blends: PineOrange, using 2 quarts of
ID: 2874444 • Letter: T
Question
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) 970 quarts of pineapple juice, 850 quarts of orange juice, 420 quarts of kiwi juice
(b) 740 quarts of pineapple juice, 920 quarts of orange juice, 380 quarts of kiwi juice
(c) A quarts of pineapple juice, B quarts of orange juice, C quarts of kiwi juice
Explanation / Answer
The equations can be written as
Let the amount of Pine Orange be x
Let the amount of Pine Kiwi be y
Let the amount of Orange kiwi be z
a)
Constraints:
2x + 3y = 970
2x + 3z = 850
y + z = 420
adding equation 1 and 2 we get
4x + 3(y+z) = 970 + 850
4x + 3 * 420 = 1820
4x = 560
x = 140
280 + 3y = 950
3y = 670
y = 230
z = 420 - 230 = 190
b)
Constraints:
2x + 3y = 740
2x + 3z = 920
y + z = 380
adding equation 1 and 2 we get
4x + 3(y+z) = 740+ 920
4x + 3 * 380= 1660
4x = 520
x = 130
260+ 3y = 740
3y = 480
y = 160
z = 380- 160= 220
c)
Constraints:
2x + 3y = A
2x + 3z = B
y + z = C
adding equation 1 and 2 we get
4x + 3(y+z) = A + B
4x + 3 * C= A+B
4x = A+B-3C
x = (A+B-3C)/4
(A+B-3C)/2 + 3y = A
3y = A/2 - B/2 + 3C/2
y = (A-B+3C)/6
z = C - (A-B+3C)/6
z = C/2 - A/6 + B/6
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.