Problem:
A cement manufacturer manufactures two kinds of cement, namely powder and granules. He can’t 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 should produce at least 500 bags of powdered cement per day. He is further restricted by a shortage of time - the granulated cement needs twice as much time to make as the powdered cement. A bag of powdered cement needs 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 powdered cement.
Required:
problem1. Formulate the LP problem of deciding how much the manufacturer must manufacture.
problem2. Work out this linear program graphically.
problem3. Which resources aren’t completely used by your solution?