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.

Practical Management Science
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ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Problem 33P: Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand...
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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
(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.

Expert Solution
Step 1

Let supply be x

Let demand be y

Assuming that the company supplies the shoes with OT and RT in the next six months. 

Step 2

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)

Total supply cost = (x1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12)=200+100+200+100+200+100+200+100+200+100+200+100= 1800

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