Solve this 2 operation research questions
natsa_
Problem 1.
A contractor estimates that the size of the workforce needed over the next 6 weeks is
4, 7, 9, 5, 6, and 7 workers, respectively.
Excess labor kept on the force will cost $400 per worker per week, and new hiring (including week 1) in any week will incur a fixed cost of $200 plus $300 per worker. The cost of firing is $100 per worker.
Find the optimal hiring schedule (check lecture note 34 for a sample format of a hiring schedule) using Backward Recursion DP. You need to include all steps.
Problem 2
The ABC Mall conducts special events to attract potential patrons. Among the events that seem to attract teenagers, the young/middle aged group, the senior citizens, the two most popular are band concerts and art shows. Their costs per presentation are $ 2000 and $4500, respectively. The total (strict) annual budget allocated to the two events is $20,000. The mall manager estimates the attendance as follows:
Number attending per presentation: Event Teenagers Band concert 150
Art Show 60
Young/middle age seniors 90 10 350 250
The manager has set minimum goals of 900, 1500 and 800 for the attendance of teenagers, the young/middle-aged group, and seniors, respectively. Formulate the problem as a goal programming (GP) model (use the Weights method to develop the objective function of the GP, feel free to make any reasonable assumption).
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