A manufacturer of high-voltage switches projects demand (in units) for the upcoming year to be as follows.
JAN 1000 FEB 1000 MAR 1000 APRIL 2000 MAY 2400 JUNE 2500 JULY 3200 AUG 2000 SEP 1000 OCT 900 NOV 800 DEC 800
The plant runs 160 hours per month and produces at an average rate of 10 switches per hour. Unit profit per switch sold is $50, and the estimated cost to hold a switch in inventory for one -month is $5. There is no inventory at the start of the year.
Overtime can be used at a cost of $300 per hour. Compute a production strategy by solving a linear program to maximize profit (i.e., net sales revenue minus inventory carrying cost minus overtime cost). Is the amount of overtime in the plan reasonable? If no, what changes to the LP model could be made to generate a more reasonable solution?