A manufacturer of high-voltage switches projects demand (in units) for the upcoming year to be as follows. Jan 1,000 Jul 3,200 Feb 1,000 Aug 2,000 Mar 1,000 Sep 1,000 Apr 2,000 Oct 900 May 2,400 Nov 800 Jun 2,500 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?