The Production Problem of NSC
NSC has received orders for steel for each of the next four
months, as given in Table 1. NSC can meet these demands by
producing the steel, by drawing from inventory, or by any
combination thereof. Because of the inflationary production
costs given in Table 1, NSC can produce more steel than needed
in each month, up to a maximum of 4000 tons. All production
takes place at the beginning of the month, after which the
demand is met and the remaining steel is stored in inventory, at
a cost of $120 per ton for one month. Also, each ton of increased
or decreased production from one month to the next incurs an
additional change-in-production cost of $50, except for the first
month, which is exempt. Given that the inventory at the
beginning of the first month is 1000 tons, formulate a four-month
production plan that ensures at least 1500 tons in inventory at the
end of the fourth month.