Problema Solution
Cindy’s Convections makes to raisin-nut mixtures. A box of mix A contains 6 ounces of peanuts, 2 ounce of raisins, and 4 ounces of cashews and sells for $3.50. A box of mix B contains 12 ounces of peanuts, 3 ounces of raisins, and 5 ounces of cashews and sells for $4.75. Cindy’s has 5400 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 'p' represent peanuts, 'r' represent raisins and 'c' represent cashews, then we have the following cost equations:
6p + 2r + 4c = 3.50
12p + 3r + 5c = 4.75
our total quantities:
5400p + 1200r + 2400c
if only mix A were made:
5400/6. = 900.0
1200/2. = 600.0
2400/4. = 600.0
...600 units could be produced
if only mix B were made:
5400/12. = 450.0
1200/3. = 400.0
2400/5. = 480.0
...400 units could be produced
...in each instance, raisins are the limiting factor, so we maximize profit taking only raisins into account
let 'x' represent the ounces of raisins used for mix A, then '1200-x' represents the amount of raisins used for mix B:
3.5 * x/2 = revenue from mix A
4.75 * (1200-x)/3 = revenue from mix B
we set these expression equal to each other to find the point of intersection:
3.5 * x/2 = 4.75*(1200-x)/3
x=570
1200-570 = 630
Cindy's should make 570 ounces of mix A and 630 ounces of mix B