NSC has received order for steel for each of the next four months, as
given in the table below. 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 the table, 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 changeinproduction cost of $50, except for the first
month, which is exempt.
Given that the inventory at the beginning of the first month is 1000 tons, formulate a
fourmonth production plan that ensures at least 1500 tons of inventory at the end of the
fourth month.
Month 1
Month 2
Month 3
Month 4
Demand (tons)
2400
2200
2700
2500
Production Costs ($/ton) 7400
7500
7600
7800
Inventory Costs ($/ton) 120
120
120
120
