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

Month	Jul	Aug	Sep	Oct	Nov	Dec
Demand (Units)	5700	6700	7400	7000	8100	6500
Working days	20	22	22	20	22	21

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.

(a) Formulate the above planning problem into an optimisation problem.

(i) State the assumptions and provide justifications if necessary.

(ii) State the decision variables, objective and constraints. Use proper notations to denote decision variables and related parameters

(iii) Use notations in (ii) to construct objective function and constraints according to the standard optimisation problem formulation.

(b) 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?