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.

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.

Month	Demand Forecast
January	10,000
February	11,000
March	15,000
April	18,000
May	25,000
June	26,000
July	30,000
August	29,000
September	21,000
October	18,000
November	14,000
December	11,000

1. What is the optimal production plan for the year if we assume no promotions? What is the annual profit from this plan? What is the cost of this plan?

2. Consider Lavare's data from Exercise 1. We now assume from Lavare that the size of the workforce can be changed by laying in and out or hiring employees. Hiring a new employee would incur a cost of $1,000; firing an employee would incur a layoff cost of $2,000. A sort of. What is the optimal production plan for the year Consumption changes in a certain way neither sees purchases assumes no promotions? What is the annual profit of this plan? What is the cost of this program?

3. Go back to Lavare's data from Exercise 1. Now, suppose a third party offers to manufacture the sinks for $74 each. In the absence of promotions, how does this change affect the optimal production plan How does this change affect the optimal timing of a promotion? Explain the changes. ('no promotion' version, ignore the word 'optimal')

NOTE: DO NOT USE SOLVER FOR THIS ASSIGNMENT.

However, in your calculations, consider not only that the objective is to end the year with 5000 units on hand, but also that it would be appropriate to start each month with an inventory level no less than 10% of that month's demand.