QUESTION

1.1 Linear Programming (LP) is a widely used mathematical modeling techniques designed to help managers in planning and decision making relative to resource allocation

(a) What are the main properties of all LP problems?

(b) What are the main assumptions of LP problems?

(c) Discuss the four special cases and difficulties that may arise when using the graphical approach to solving LP problems

1.2 A cement manufacturer produces two types of cement, namely granules and powder. He cannot make more than 1600 bags a day due to a shortage of vehicles to transport the cement out of the plant. A sales contract means that he must produce at least 500 bags of powdered cement per day. He is further restricted by a shortage of time - the granulated cement requires twice as much time to make as the powdered cement. A bag of powdered cement requires 0.24 minutes to make and the plant operates an 8 hour day. His profit is £4 per bag for granulated cement and £3 per bag for the powdered cement

(a) Formulate the problem of deciding how much he should produce as a linear program

(b) Solve this linear program graphically