Answer:
Explanation:
A Balanced Transportation Problem is a Transportation Problem in which the Total Supply equals the Total Demand. If a transportation problem is unbalanced due to Shortage of Supply, it is converted to a Balanced Transportation Problem with the creation of a Dummy Supply Point, with zero cost attached from each Demand Point to the Dummy Supply Point, provided there is no penalty attached.
The U.S. government auctions off oil leases at two sites: 1 and 2.
Define the supply points as:
Point 1 = acres of land to be auctioned at site 1 (s1)
Point 2 = acres of land to be auctioned at site 2(s2)
Since, at each site 100,000 acres of land are to be auctioned, therefore
s1 = 100000
s2 = 100000
Define demand points as follows:
Point 1 = 8acres of land bidder Cliff Ewing can receive (d1)
Point 2 = acres of land bidder Blake Barnes can receive(d2)
Point 3 = acres of land bidder Alexis Pickens can receive (d3)
Since, according to the government rule no bidder can receive more that 40% of the land auctioned at one site, therefore,
d1 =80000
d2 = 80000
d3 = 80000
Therefore, the total supply is:
100000 + 100000 = 200000
The total demand is:
80000 + 80000 + 80000 = 240000
Thus, Total Demand > Total Supply
Therefore there is a shortage of 40000 acres of land. The transportation problem is unbalanced.
To balance the problem add a dummy ‘Supply point’ s3 with a supply equal to the shortage, that is, 40000 acres.
Let,c11 be the revenue from bidder j opting site i.
Cliff bids $1,000/acre for site c1 land and $2,000/acre for site c2 land.
c11 = 1000
c21 = 2000
Blake bids $900/acre for site s1 land and $2,200/acre for site s2 land.
c12 = 900
c22 = 2200
Alexis bids $1,100/acre for site s1 land and $1,900/acre for site s2 land.
c13 =1100
c23 = 1900
also
c 31=0 c32 =0 c33 =0
