HMK is a handbag making company. They have a forecasting team which provides them thedemand forecast for their product. The report provided by the forecasting team indicates the demand forecast for the next 6 months. The summary is provided in the table below:
Month Demand (units)
March 5000
April 6000
May 5000
June 9000
July 6000
Aug 5000
It takes a handbag maker 15 minutes to produce a handbag. Each handbag maker works 150hours per month plus up to 40 hours per month of overtime. The monthly regular salary for a handbag maker is $2000. But they get paid an extra $50 for each hour they work overtime .At the beginning of each month, HMK can either hire or fire workers. It costs the company$1800 to hire a worker and $2200 to fire a worker. The monthly holding cost per handbag is 3%of the cost of producing it with regular-time labour. The raw materials in each handbag cost $10.
Formulate an LP that minimizes the cost of meeting (on time) the demands of the next six months. At the beginning of month 1, HMK has 13 workers.