Problema Solution
A box of mix A contains 6 ounces of peanuts, 2 ounces of raisins, and 4 ounces of cashews and sells $3.50. A box mix of B contains 12 ounces of peanuts, 3 ounces of raisins, and 5 ounces of cashews and sells for $4.75. Cindy has 54,000 ounces of peanuts, 1200 ounces of raisins, and 2400 ounces of cashews available. How many of each mix should they make to maximize revenue?
Answer provided by our tutors
let
x = oz of the first $3.50 mix
y = oz of the second $4.75 mix
the revenue r = 3.50x + 4.75y
(6/(6 + 2 + 4))x + (12/(12 + 3 + 5))y <= 54000
(2/(6 + 2 + 4))x + (3/(12 + 3 + 5))y <= 12000
(4/(6 + 2 + 4))x + (5/(12 + 3 + 5))y <= 2400
or
(1/2)x + (3/5)y <= 54000
(1/6)x + (3/20)y <= 12000
(1/3)x + (1/4)y <= 2400
and also
x >= 0
y >= 0
click here to see the graph
for x = 7200, y = 0
r = 3.50*7200
r = $25,200
for x = 0, y = 9600
y = 4.75*9600
y = $45,600
to maximize the revenue they should make 9600 oz of the second mix.