(Material blending problem) Amalgamated Products

has just received a contract to construct steel

body frames for automobiles that are to be produced

at a new Japanese auto factory in Tennessee. The

Japanese auto manufacturer has strict quality control

standards for all of its component subcontractors

and has informed Amalgamated that each frame

must have the following steel content:

MATERIAL

MINIMUM

PERCENTAGE

MAXIMUM

PERCENTAGE

Manganese 2.1 2.3

Silicon 4.3 4.6

Carbon 5.05 5.35

Amalgamated mixes batches of eight different

available materials to produce 1 ton of steel for use

in the body frames. The table on this page details

these materials.

Formulate and solve the LP problem, indicating

how much of each of the eight materials should be

blended into a 1-ton load of steel so that Amalgamated

meets its requirements while minimizing costs ( PLEASE PLEASE SHOW ALL THE CONTRAINTS IN THE LP WINDOW YOU WILL USE EXCELQM THANK YOU) The table goes like this Material Magnanese, Minimum percentage is 2.1 and Maximum percentage 2.3 Material SiliconMinimum percentage is 4.3 and maximum percentage is 4.6. Material carbon Minimum percentage 5.05 and Maximum percentage is 5.35

_{MATERIAL AVAIL. MANGANESE(%)SILICON(%)CARBON(%)POUNDS AVAIL. COST PER POUND($)}

_{Alloy 1 70.0 15.0 3.0 No limit 0.12}

_{Alloy 2 55.0 30.0 1.0 300 0.13}

_{Alloy 3 12.0 26.0 0 No limit 0.15}

_{Iron 1 1.0 10.0 3.0 No limit 0.09}

_{Iron 2 5.0 2.5 0 No limit 0.07}

_{Carbide 1 0 24.0 18.0 50 0.10}

_{Carbide 2 0 25.0 20.0 200 0.12}

_{Carbide 3 0 23.0 25.0 100 0.09}