Web Mercantile sells many household products through an online catalog. The comp
ID: 370623 • Letter: W
Question
Web Mercantile sells many household products through an online catalog. The company needs substantial warehouse space for storing its goods. Plans now are being made for leasing warehouse storage space over the next 5 months. Just how much space will be required in each of these months is known. However, since these space requirements are quite different, it may be most economical to lease only the amount needed each month on a month-by-month basis. On the other hand, the additional cost for leasing space for additional months is much less than for the first month, so it may be less expensive to lease the maximum amount needed for the entire 5 months. Another option is the intermediate approach of changing the total amount of space leased (by adding a new lease and/or having an old lease expire) at least once but not every month.
The space requirement and the leasing costs for the various leasing periods are as follows:
Solve this model by simplex method and determine the minimum leasing cost for meeting the space requirement.
$57,700,000
$63,400,000
$76,500,000
$84,100,000
a.$57,700,000
b.$63,400,000
c.$76,500,000
d.$84,100,000
Month Required Leasing Period Cost per Sa Ft Space (Sqa.Ft) Months) 30,000 20,000 40,000 10,000 50,000 Leased $650 $1000 $1350 $1600 $1900 2 4 4 5Explanation / Answer
a) Let xij= the amount of space leased in month
i for a period of j months for i= 1, ...,5 and j= 1, ...,6i
Minimize
C= 650(x11+x21+x31+x41+x51) + 1000(x12+x22+x32+x42)
+1350(x13+x23+x33) + 1600(x14+x24) + 1900x15
subject to x11+x12+x13+x14+x1530,000
x12+x13+x14+x15+x21+x22+x23+x2420,000
x13+x14+x15+x22+x23+x24+x31+x32+x3340,000
x14+x15+x23+x24+x32+x33+x41+x4210,000
x15+x24+x33+x42+x5150,000
andxij0,fori= 1, ...,5 andj= 1, ...,6i.
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