In preparation for winter season, a clothing company is manufacturing overcoats for the entire family — women, men, and children. The company is trying to decide what combination of these three types of overcoats to produce.

The company hired full- time workers and part-time workers for manufacturing process. Each fulltime worker works a 40-hour week. Furthermore, the number of full-time workers can never drop below 20. Each part-time worker works 20 hours per week and there must be at least 2 full-time workers for each part-time worker.

All three types of overcoats are made out of the same 100% wool. The company has a contract with a supplier of the wool, and receives a 7,500 square feet shipment of the material each week. The material requirements and labour requirements, along with the gross profit per overcoat sold (not considering labor costs) are given in the following table.

Gross Profit (per Coat)	Labor Required (minutes)	Material Required (square feet)	overcoats
8$	30	2	Men's
10$	45	1,5	Women's
6$	40	1	Children's

Each full-time worker earns $15 per hour, while each part-time worker earns $11 per hour. The company wishes to know what combination of each of the three types of winter coats to produce per week, as well as how many full-time and how many part-time workers to employ. The company would like to maximize their net profit, their gross profit from sales and their labour costs.