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Question 2: 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 coming year. Anticipated monthly demand from distributors over the 12 months is shown in the table below. Capacity at Lavare is governed by the number of machine operators it hires. The firm works 20 days per month with a regular operating shift of eight hours per day. Any time beyond that is considered overtime. Regular-time pay is $17 per hour, and overtime is $24 per hour. ssume that regular-time labor cost is calculated based on full employment - where each employed worker is paid for a full 160 hours per month regardless of how much of that available time is utilized for production. Overtime labor cost is computed on a per-hour basis as usual. Overtime is limited to 20 hours per month per employee. The plant currently has 257 employees. Each sink requires two hours of labor input. It costs $4 to carry a sink in inventory from one month to another. Materials cost per sink is $39, and sinks are sold to distributors for $125 cach. We assume that no stockouts are allowed and the starting inventory in January is 5,000 units and the desired ending inventory in December is also 5,000 units. Lavare can change the size of its workforce each month as follows. Hiring a new employee costs $1,000; laying off an employee incurs a cost of $2,000. Determine the optimal production plan for the year and its total cost. [40 points]