Lavare, a major manufacturer of stainless steel sinks, anticipates demand from distributors over the 2 months is10k, 15k, respectively. Capacity is governed by the number of 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 over time is $22 per hour. Overtime is limited to 20 hours per month per employee. 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 $125 each. We assume that no stockouts are allowed and the starting inventory is 5k units. The plant currently has 250 workers. Hiring a new employee incurs a cost of $1000; laying off an employee incurs a layoff cost of $2000. Formulate the above operations planning problem as an optimization problem by writing down the decisions variables, the objective function, and the constraints.