Q1(a) Construct an objective function for the weighted
programming model by the following goals. (b) Construct a
preemptive programming model by the following goals.
Q1 A Construct An Objective Function For The Weighted Programming Model By The Following Goals B Construct A Preempt 1 (113.94 KiB) Viewed 40 times
Q1. ABC Disk Company with the weekly expenses of RM500 has four full-time workers and three part-time workers. Each full-time worker is paid RM 6 per hour and each part-time worker is paid RM 4 per hour. Without overtime, each full-time and part- time workers need to work up to 40 hours per week and 20 hours per week, respectively. Each full-time worker who works for overtime will be paid RM 8 per hour. A full time worker can sell 6 disks per hour and a part-time worker can sell 3 disks per hour. The selling price and the cost of each disk are RM 9 and RM 6 respectively. (a) Construct an objective function for the weighted programming model if the ABC Disk Company sets the following goals as: Goal 1: Sell at least 1100 disks per week. The penalty of RM100 will be incurred for each unit it falls short of this goal. Goal 2: Earn a profit of at least RM 1000 per week. The penalty of RM200 will be incurred for each ringgit it falls short of this goal. Goal 3: The overtime is limited to 35 hours per week for full-time workers. The penalty of RM50 will be incurred for each unit it falls short of this goal. (10 marks) (b) Construct a preemptive programming model if the ABC Disk Company sets the following goals according to the order of importance: Goal 1: The number of hours to work less than 40 hours per week for all full- time workers should be minimized. Goal 2: The overtime is limited to 35 hours per week for full-time workers. Goal 3: Earn a profit of at least RM 1000 per week. Goal 4: Meet the weekly working hours for part-time workers. (15 marks) [Total 25 marks]
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