Question

The U.S. government auctioning off oil leases at two sites: 1 and 2. At each site, 100,000 acres of land are to be auctioned. Cliff Ewing, Blake Barnes, and Alexis Pickens are bidding for the oil. Government rules state that no bidder can receive more than 40% of the land being auctioned. Cliff has bid $1,000/acre for site 1 land and $2,000/acre for site 2 land. Blake has bid $900/acre for site 1 land and $2,200/acre for site 2 land. Alexis has bid $1,100/acre for site 1 land and $1,900/acre for site 2 land. Formulate a balanced Consider the following network. (a) Formulate a balanced transportation model to maximize the government's revenue. (b) Find an initial solution by using northwest corner method. (c) Use the transportation simplex method to find an optimal solution using the bfs found in part (b).

Answer 1

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