# Optimizing problem

#### iNCREDiBLE

I'm stuck on this optimizing problem:

Tarmac Chemical Corporation produces a special chemical compound—called CHEMIX—that is used extensively in high school chemistry classes. This compound must contain at least 20% sulfur, at least 30% iron oxide, and at least 30% but no more than 45% potassium. Tarmac’s marketing department has estimated that it will need at least 600 pounds of this compound to meet the expected demand during the coming school session. Tarmac can buy three compounds to mix together to produce CHEMIX. The makeup of these compounds is show in the following table.

Compounds 1,2 and 3 cost $5.00,$5.25, and \$5.50 per pound, respectively. Tarmac wants to use an LP model to determine the least costly way of producing enough CHEMIX to meet the demand expected for the coming year.

Compound 1: 20% Sulfur, 60% Iron Oxide, 20% Potassium.
Compund 2: 40% Sulfur, 30% Iron Oxide, 30% Potassium.
Compund 3: 10% Sulfur, 40% Iron Oxide, 50% Potassium.

a) Formulate a LP model for this problem.
b) What is the optimal solution?

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#### mathmike

CAN YOU ATLEAST GIVE IT A TRY BEFORE I HELP YOU. YOU SHOULD START WITH SOMETHING LIKE dy/dv = v1 + v2 + v3
then find equations for v1,v2,v3

v1 = volume compound 1 and so on

#### Hurkyl

Staff Emeritus
Gold Member
All yelling aside, mathmike is right: we will gladly help you do the problem, but we will not do it for you.

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