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.

Fanning company is considering the addition of a new product to its cosmetics line. the company has three distinctly different options: a skin cream, a bath oil, or a hair coloring gel. relevant information and budgeted annual income statements for each of the products follow. skin cream bath oil color gel budgeted sales in units (a) 110,000 190,000 70,000 expected sales price (b) $8 $4 $11 variable costs per unit (c) $2 $2 $7 income statements sales revenue (a × b) $880,000 $760,000 $770,000 variable costs (a × c) (220,000) (380,000) (490,000) contribution margin 660,000 380,000 280,000 fixed costs (432,000) (240,000) (76,000) net income $228,000 $140,000 $204,000 required: (a) determine the margin of safety as a percentage for each product. (b) prepare revised income statements for each product, assuming a 20 percent increase in the budgeted sales volume. (c) for each product, determine the percentage change in net income that results from the 20 percent increase in sales. (d) assuming that management is pessimistic and risk averse, which product should the company add to its cosmetics line? (e) assuming that management is optimistic and risk aggressive, which product should the company add to its cosmetics line?