Amber Foods is an online restaurant that delivers meals on demand from its own menu. To better plan its manpower resources, the restaurant has conducted a demand forecast for the coming 6 months as follows: Month Demand (meals) Days Jul 3,100 31 Aug 4,200 31 Sep 3,300 30 Oct 3,580 31 Nov 3,700 30 Dec 4,300 31 The "demand refers to the estimated number of meals ordered by customers in a month, and "days refer to the number of days for service. The restaurant currently has 11 employees, 7 of which are responsible for food preparation and 4 of them are responsible for delivery. On average, one food preparation employee can complete 22 meals a day, and one delivery employee can deliver 30 meals a day. Each employee works 5 days a week. The restaurant can choose to hire or lay off employees during the 6-month period. Newly hired employees need training and practice to achieve the same productivity as the old employee. For food preparation position, it is estimated that a new employee achieves 65% of existing employee's productivity in the first month of employment and achieves 100% from the second month onwards. For delivery position, it is estimated that a new employee achieves 80% of productivity in the first month and 100% from the second month onwards. On average, a meal can generate a revenue of $41. The average material cost of a meal is $17. The average salary for a food preparation employee is $2,600/month, the average salary for a delivery employee is $2,100/month. The hiring and training cost of a new food preparation employee is $900, and that cost of a new delivery staff is $380. The layoff cost of a food preparation employee and a delivery employee are $1,800 and $1,350 respectively. To ensure the stability of workforce and maintain employee morale, the company has a human resource policy that the maximum hiring or firing is one headcount per month per position. Unfulfilled demand will be lost, i.e., that is no backorder. It is estimated that every unfulfilled meal incurs a loss of goodwill of $4. Question 1 Formulate the above planning problem into an optimisation problem. You should do the following: (a) State the assumptions for the formulation and provide justifications if necessary. (9 marks) (b) State the decision variables, objective and constraints. Use proper notations to denote decision variables and other related parameters. (35 marks) (c) Use notations in Q1(b) to construct objective function and constraints according to the standard optimisation problem formulation. (21 marks)