Given a certain forecast, aggregate planning is to determine operational parameters over a specified time horizon, such as production rate, workforce size, machine capacity level, inventory, etc. a) The fundamental trade-offs in aggregate planning are among capacity (regular time, overtime, subcontracted), inventory and backlog/lost sales because of delay. Briefly explain the three strategies that are most widely used in aggregate planning. [6] b) A gardening tool company aims to establish an aggregate plan to minimise its operation cost in the next month, in terms of units of production, units of subcontracted, number of overtime hours, and inventory (at the end of the next month). Formulate a mathematical optimisation problem for this company by using the information below. You may wish to define extra variables as necessary. Workforce. The company pays a monthly cost of 1000 for each of the W workers, and decides not to hire or to lay off any workers in the month. Each worker can produce 40 units per month on regular time. Overtime. Overtime labour cost is 12 per hour per worker. Every four hours of overtime per worker can produce one unit. No one can work more than 10 hours of overtime each month. Inventory. At the beginning of the month the inventory is 1000 units. The inventory cost for a certain month is calculated from the average at the beginning and the end of that month. The actual cost is 2 per unit per month. The company decides that at the end of next month the inventory must be more than 500 units. Production. Production cost is 10 per unit. Subcontract. Subcontracted production cost is 30 per unit. Demand. The demand for the next month has been forecasted to be 1500 units.