Question

The government is auctioning off oil leases at two sites. At each site, 150,000
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 45% of the land being auctioned. Cliff has bid $2000 per
acre for site 1 land and $1000 per acre for site 2 land. Blake has bid $1800
per acre for site 1 land and $1500 per acre for site 2 land. Alexis has bid
$1900 per acre for site 1 land and $1300 per acre for site 2 land.
a. Determine how to maximize the government’s revenue with a
transportation model.
b. Use SolverTable to see how changes in the government’s rule on 45%
of all land being auctioned affect the optimal revenue. Why can the
optimal revenue not decrease if this percentage required increases?
Why can the optimal revenue not increase if this percentage required
decreases?

Answer 1

a. The Solved solution in Excel is

The Solver dialog will be like this

b.

Using different values in cell E6, different optimum values are obtained.

Max % allocation	Optimum revenue $m
35%	477.75
40%	486
45%	494.25
50%	502.5
60%	507
70%	511.5
80%	516
90%	520.5
100%	525

As the maximum percentage cap is increased, the allocation more land gets alloted at higher price, and the total revenue increases.

As the maximum percentage cap is decreased, the allocation more land gets alloted at higher price, and the total revenue decreases.