September's production was set at 12,000 units. Varying production rate incurs some cost:
production can be increased from one month to the next at a cost of $2 per unit and it can bedecreased at a cost of $0.50 per unit. In addition, inventory left at the end of a month can be
stored at a cost of $1 per unit per month. Given current demand, there will be no inventory at the
end of September. No inventory is desired at the end of January. Formulate a linear program that
minimizes the total cost (varying production rate + inventory costs) of meeting the above demand.
Exercise 51 An oil company blends gasoline from three ingredients: butane, heavy naphta and
catalytic reformate. The characteristics of the ingredients as well as minimum requirements for
regular gasoline are given below: