Consider the data for Lavare in Problem 1. We now assume that Lavare can change the size of the workforce by laying off or hiring employees. Hiring a new employee incurs a cost of $1,000; laying off an employee incurs a layoff cost of $2,000. a) What is the optimal production plan for the year if we assume no promotions? What is the annual profit with this plan? What is the cost of this plan? b) Is it better to promote in April or July? How much increase in profit can be achieved as a result? c) If the holding cost for sinks increases from $3 per month to $5 per month, does the decision of the timing of promotion change? Why or why not?

Lavare, located in the Chicago suburbs, is a major manufacturer of stainless steel sinks. Lavare is in the middle of the demand and supply planning exercise for the coming year. Anticipated monthly demand from distributors over the 12 months is shown in Table 1. Table 1 Anticipated Monthly Demand at Lavare Month Demand Month Demand Jan 10,000 July 30,000 Feb 11,000 August 29,000 March 15,000 September 21,000 April 18,000 October 18,000 May 25,000 November 14,000 June 26,000 December 11,000 Capacity at Lavare is governed by the number of machine operators it hires. The firm works 20 days a month, with a regular operating shift of eight hours per day. Any time beyond that is considered overtime. Regular-time pay is $15 per hour and overtime is $22 per hour. Overtime is limited to 20 hours per month per employee. The plant currently has 250 employees. Each sink requires two hours of labor input. It costs $3 to carry a sink in inventory for a month. Materials cost per sink is $40. Sinks are sold to distributors at a price of $125 each. We assume that no stockouts are allowed and the starting inventory entering January is 5,000 units and the desired ending inventory in December is also 5,000 units. Market research has indicated that a promotion dropping prices by 1 percent in a given month will increase sales in that month by 20 percent and bring forward 10 percent demand from each of the following two months. Thus, a 1 percent drop in price in March increases sales in March by 3,000 (= 0.2 × 15,000) and shifts 1,800 (= 0.1 × 18,000) units in demand from April and 2,500(= 0.1 × 25,000) units from May forward to March.

Period	demand
1	10,000
2	11,000
3	15,000
4	18,000
5	25,000
6	26,000
7	30,000
8	29,000
9	21,000
10	18,000
11	14,000
12	11,000