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 200 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. Let xi = pairs of shoes produced in month i using regular-time labor, yi = pairs of shoes produced in month i using overtime labor, and zi = inventory of shoes at the end of month i. Using these decision variables, formulate an LP that minimizes the total cost and meets the demand on time in the next six months.
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 200 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.
Let xi = pairs of shoes produced in month i using regular-time labor,
yi = pairs of shoes produced in month i using overtime labor, and
zi = inventory of shoes at the end of month i.
Using these decision variables, formulate an LP that minimizes the total cost and meets the demand on time in the next six months.
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