INME 323 Operations Research Laboratory Exercise No. 3

LP Programming Formulation by Prof. Rodrigo S. Jamisola Jr., Second Semester 2022-2023,

BIUST Formulating Linear Programming (LP) Models and Converting into Standard Form Instruction: Given the word problems below, convert them into linear programming models, i.e, convert into equivalent numerical models, and transform into standard form.

1. TexasCo produces aviation fuel and heating oil. Each barrel of oil costs $40 that is distilled and yields 50% aviation fuel and 50% heating oil. If sold directly without further processing, aviation fuel sells for $60/barrel and heating oil for $40/barrel. With further processing the output can be sold are a higher price. To further process aviation fuel, it will take 1 hour to process 1000 barrels and these can be sold for $130/barrel. It takes 45 minutes to further process 1000 barrels of heating oil and these can be sold for $90/barrel. Each day, at most 20,000 barrels of oil can be purchased and 8 hours of further processing are available. Formulate an LP to maximize TexasCos profit.

2. A shoemaker takes 15 minutes to produce a pair of shoes. Each shoemaker works 150 hours/month, plus up to 40 hours/month overtime. A shoemaker is paid a regular salary of $2000/month plus $50/hour for overtime. A shoemaker can be hired or fired at the beginning of a month. It costs $1500 to hire a worker and $1900 to fire a worker. The monthly holding cost per pair of shoes is 3% of the cost of producing a pair of shoes with regular-time labor. (The raw materials in a pair of shoes cost $20.) At the beginning of month 1, the shoemakers have 13 workers. Formulate the LP that minimizes the cost of meeting on time the demands of the next six months