A shoe company forecasts the following demands duringthe next six months: month 1—200; month 2—260; month3—240; month 4—340; month 5—190; month 6—150. Itcosts $7 to produce a pair of shoes with regular-time labor(RT) and $11 with overtime labor (OT). During each month,regular production is limited to 200 pairs of shoes, andovertime production is limited to 100 pairs. It costs $1 permonth to hold a pair of shoes in inventory. Formulate abalanced transportation problem to minimize the total costof meeting the next six months of demand on time.
A shoe company
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
(RT) and $11 with overtime labor (OT). 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. Formulate a
balanced transportation problem to minimize the total cost
of meeting the next six months of demand on time.
Let supply be x
Let demand be y
Assuming that the company supplies the shoes with OT and RT in the next six months.
The supply points will be:
x1= 200 (month 1 RT)
x2 = 100 (month 1 OT)
x3= 200 (month 2 RT)
x4 = 100 (month 2 OT)
x5= 200 (month 3 RT)
x6 = 100 (month 3 OT)
x7= 200 (month 4 RT)
x8 = 100 (month 4 OT)
x9= 200 (month 5 RT)
x10 = 100 (month 5 OT)
x11= 200 (month 6 RT)
x12 = 100 (month 6 OT)
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