Show me the steps to solve Task $1$: Answer the following questions. Provide answers in a $.$docx file and show screen captures if you used a software tool $($such as Excel$).$ Upload supporting files.

$1.$ Problem $1$:

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 below:

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Demand $(000)101115182526302921181811$

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 and shifts units in demand from April and units from May forward to March.

a$.$ 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?

b$.$ Is it better to promote in April or July? How much increase in profit can be achieved as a result?

c$.$ If sinks are sold for $$250$ instead of $$125,$ does the decision about the timing of the promotion change? Why?

$2.$ 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?

$3.$ Return to the data for Lavare in problem $1.$ Now, assume that a third party has offered to produce sinks at $$74$ per unit.

a$.$ How does this change affect the optimal production plan without a promotion?

b$.$ How does this change affect the optimal timing of a promotion? Explain the changes.

$4.$ Mintendo Game Girl case study:

It is late June, and Sandra Huchim, head of operations at Mintendo, and Bill Smith, head of sales of We $$R$$ Toys, are about to get together to discuss production and marketing plans for the next $6$ months. Mintendo is the manufacturer of the popular Game Girl handheld electronic game that is sold exclusively through We $$R$$ Toys retail stores. The second half of the year is critical to Game Girl$$s success, because a majority of its sales occur during the holiday shopping period.

Sandra is worried about the impact that the upcoming holiday surge in demand will have on her production line. Costs to subcontract assembly of the Game Girls are expected to increase, and she has been trying to keep costs down, given that her bonus depends on the level of production costs.

Bill is worried about competing toy stores gaining share in the handheld electronic game market during the Christmas buying season. He has seen many companies lose their share by failing to keep prices in line with the performance of their products. He would like to maximize the Game Girl market share in the handheld electronic game market.

Both Sandra$$s and Bill$$s teams produce a joint forecast of demand over the next six months, as shown in the following table:

Month Jul Aug Sep Oct Nov Dec

Demand Forecast $(000)100110130180250300$

We $$R$$ Toys sells Game Girls for $$50$ apiece. At the end of June, the company has an inventory of $50,000$ Game Girls. Capacity of the production facility is set purely by the number of workers assembling the Game Girls. At the end of June, the company has a workforce of $300$ employees, each of whom works $8$ hours of regular time at $$15/$hour for $20$ days each month. Work rules require that no employee works more than $40$ hours of overtime per month. The various costs are shown in the following table:

Item Cost

Material cost $$12/$unit

Inventory holding cost $$2/$unit$/$month

Marginal cost of a stockout $$10/$unit$/$month

Hiring and training costs $$3$