Shoemakers of america forecasts the following demand for the next six months: 5000 pairs in month 1; 6000 pairs in month 2; 7000 pairs in month 3; 9000 pairs in month 4; 6000 pairs in month 5; 5000 pairs in month 6. it takes a shoemakers half an hour to produce a pair of shoes. each shoemaker works 150 hours per month plus up to 40 hours per month of overtime. a shoemaker is paid a regular salary of $2000 per month plus $20 per hour for overtime. at the beginning of each month, shoemakers can either hire or fire workers. it costs the company $1000 to hire a worker and $1200 to fire a worker. if there is any leftover inventory at the end of the month, the monthly holding cost per pair of shoes is $1.20. the raw materials in a pair of shoes cost $10. at the beginning of month 1, shoemakers has 15 workers and 500 pairs of shoes in inventory.

determine how to minimize the cost of meeting (on time) the demands the next six months.