Solving Tarmac Chemical Corp's Optimizing Problem with a LP Model

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In summary, Tarmac Chemical Corporation produces a chemical compound called CHEMIX for high school chemistry classes. It must contain at least 20% sulfur, at least 30% iron oxide, and at least 30% but no more than 45% potassium. The company can buy three compounds to mix together to produce CHEMIX, with varying costs per pound. The objective is to use a LP model to determine the least costly way of producing enough CHEMIX to meet the expected demand of at least 600 pounds. The LP model should involve equations for the volume of each compound (v1, v2, v3) and the optimal solution should be determined.
  • #1
iNCREDiBLE
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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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  • #2
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
 
  • #3
All yelling aside, mathmike is right: we will gladly help you do the problem, but we will not do it for you.
 

What is Tarmac Chemical Corp's optimizing problem?

Tarmac Chemical Corp's optimizing problem involves finding the best way to allocate their resources in order to maximize their profits. This includes determining the optimal production levels for each of their products, while taking into account constraints such as limited resources and market demand.

Why is a LP model used to solve this problem?

A LP (linear programming) model is used because it is a mathematical optimization technique that can handle multiple decision variables and constraints in a linear fashion. This makes it well-suited for solving complex business problems, such as Tarmac Chemical Corp's optimizing problem.

What are the main steps involved in solving this problem with a LP model?

The main steps involved in solving this problem with a LP model are: formulating the objective function, identifying decision variables and constraints, setting up the LP model, solving the model using appropriate software, and interpreting the results to make decisions.

What are some potential challenges in solving this problem with a LP model?

Some potential challenges in solving this problem with a LP model include: identifying all relevant decision variables and constraints, formulating an accurate objective function, and ensuring the model is realistic and reflective of the actual business operations of Tarmac Chemical Corp.

What are the benefits of using a LP model to solve this problem?

The benefits of using a LP model to solve this problem include: the ability to find the optimal solution quickly and efficiently, the ability to consider multiple constraints and objectives simultaneously, and the ability to easily adjust the model as needed to reflect changes in the business environment.

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