Question

You have decided to enter the candy business. You are considering producing two types of candies: A and B, both of which consist solely of sugar, nuts, and chocolate. At present, you have in stock 12,000 ounces of sugar, 3,000 ounces of nuts, and 3,000 ounces of chocolate. The mixture used to make candy A must contain at least 10% nuts and 10% chocolate. The mixture used to make candy B must contain at least 20% nuts. Each ounce of candy A can be sold for $0.40 and each ounce of candy for $0.50. Determine how you can maximize your revenues from candy sales.

Answer 1

Let ingredient 1 = sugar,
Let ingredient 2 = nuts,
Let ingredient 3 = chocolate,
Let candy 1 = Type B, and
Let candy 2 = Type A

Let xij
ounces of ingredient (i)
used to make candy (j)
(All variables are in ounces.)

The appropriate LP is

max z = 0.50(X12 + X22 + X32) x 0.40(X11 + X21 + X31)

s.t.
X11 + X12 <= 12000.............(Sugar constraint)
X21 + X22 <= 3000.............. (Nuts constraint)
X31 + X32 <= 3000 ..............(Chocolate constraint)

X22 >= 0.2(X12 + X22 + X32)
X21 >= 0.1(X11 + X21 + X31)
X31 >= 0.1(X11 + X21 + X31)

All variables >= 0

Note = X11 mean sugar(1) in TypeB (1) candy