A shoe company forecasts the following demands during the next six months: month 1 – 200; month 2 – 260; month 3 – 240; month 4 – 340; month 5 – 190; month 6 – 150. It costs $7 to produce a pair of shoes with regular-time labor and $11 with overtime labor. During each month, regular production is limited to 180 pairs of shoes, and overtime production is limited to 100 pairs. It costs $1 per month to hold a pair of shoes in inventory. The initial inventory is 0.
Formulate an LP to determine a production plan which minimizes the total cost and meets the demand on time in the next six months.
In order to get full points, your mathematical LP model must include the definition of decision variables, objective function and all constraints needed.