A manufacturer of electronic home appliances receives the following estimates of demand requirements in a 6-month period as follows:

The "demand" refers to the quantities of product ordered by customers in a month, and "days" refer to the number of working days (exclusive of public holidays) in a month.

The company currently hires 16 employees in its production site. On average, one employee can produce 19 units of product per working day. To adjust its production operations, the company allows undertime and overtime. For example, there are 20 working days in July. If an employee works 18 days in July, then he has 2 days of undertime and 0 days of overtime; if he works 21 days in July, then he has 0 days of undertime and 1 day of overtime. According to the human resource policy, the maximum allowable overtime is 2 days per month per employee. The overtime payment is $357 per day per employee on average.

On average, one unit of product generates a revenue of $237. The average material cost of one unit of product is $89. Employees are paid on fixed salary and the average salary for an employee is $4,000/month. An order that is unfulfilled (in the month when it was received) is considered as backorders, which would incur a backorder cost of $42 per unit of product per month. Unsold finished products are stored in warehouse and incurs inventory holding cost of $34 per unit per month. Assume that the initial inventory at the beginning of July is 1,200 units.

Use Microsoft Excel Solver to solve the optimisation problem and answer the following questions.

(i) Select the appropriate solving method and provide justification.

(ii) Clearly present the relevant Excel output. Based on the output, what is the company's aggregate plan for the 6-month period? Are there any months with inventory/backorders? What is the objective function value?