EXECUTIVE SUMMARY

Problem Definition:

The Gartland Steel Company is a leading manufacturer of Steel of the United States. A new

Objectives:

Without pollution from coal and ore yard:

1. Identify the input-output mix at the present levels of pollution ie., 5525 thousand pounds/year.

2. Identify the input-output mix at the desired levels of pollution ie., 5163 thousand pounds/year.

3. Identify the change in profits when the mix in the open hearth furnaces is changed. Include pollution from coke and ore yard into the Linear program

Include pollution from coal and ore yard

4. Identify the input-output mix at the present levels of pollution ie., 5525 thousand pounds/year.

5. Identify the input-output mix at the desired levels of pollution ie., 5163 thousand pounds/year.

6. Identify the change in profits when the mix in the open hearth furnaces is changed.

Linear Program Formulation:

The linear program was formulated using the following rules obtained from the case data.

The ratio of inputs to outputs at any processing unit (such as coking plant, blast furnace etc..) shall be in the ratio as per the requirement and output given in the table.

Ex: Consider the table given below

Sinter Plant Blast Furnace1 ton of outputs Sinter Pig IronProduces scrap (tons) -- 0.01Produces particulate pollution (pounds)

0.777 0.474

Requires (tons) 0.52 Ore

1.12Ore

0.65Coke

0.47Sinter

Operating Costs $18.77 $57.82Coast of coal and ore used $18.82 $40.54Energy Credits $0.00 $0.16

Under Sinter Plant, it shows that for producing 1 ton of Sinter, it takes 0.52 ton of ore.

Representing the same in the form of an equation, we obtain the following equation

x sinter= xore0.52

This equation can be further reduced to the following to make it easier to use with excel solver.

0.52 xsinter−xore=0

So the coefficients of the variables xsinter and xore will be 0.52 and -1 respectively and the constraint equation will be equated to 0.

A similar process is followed throughout