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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 bid- ding 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?

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 bid- ding 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?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section: Chapter Questions
Problem 56P
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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 bid- ding 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?

22 27 1 Oil lease auction 2 3 Bids for sites (dollars/acre) 4 5 Ewing 6 Bames 7 Pickens 8 9 Max % that can be sold to any bidder 10 11 Number of acres sold to bidders 12 13 Ewing 14 Bares 15 Pickens 16 Total 17 18 Available 19 20 Revenue ($millions) 21 22 23 24 25 26 28 29 30 31 32 al 33 C 34 35 36 37 38 39 40 Point X Retiremen nnin iont vrav A P5-43 fx | P5-46 COOOO 2000 1800 1900 135000 0 0 =SUM(B13:B15) 150000 B 1-SUMPRODUCT(B5:C7,B13:C15) P5-46 part B JUL 5 P5-52 Site 1 Site 1 B 1000 1500 1300 0.45 0 135000 0 + =SUM(C13:C15) 150000 C Site 2 Site 2 Geography =SUM(B13:C13) -SUM(B14:C14) =SUM(B15:C15) =B18+C18 D Set Objective: To: O Max Total N< $B$20 4 db Min By Changing Variable Cells: $B$13:$C$15 Sort <= <= KE Solver Parameters Subject to the Constraints: $B$16:$C$16 <= $F$13:$F$14 $D$13:$D$15 <= $B$18:$D$18 S E Filter Make Unconstrained Variables Non-Negative Select a Solving Method: Simplex LP Value Of: =$D$18*$C$9 =$D$18*$C$9 =$D$18*$C$9 л Reapply Advanced 0 F Max allowed Add Change Delete Reset All Load/Save Options Text to Columns 18 30 G ((( Wha Anal X DE
Transcribed Image Text:22 27 1 Oil lease auction 2 3 Bids for sites (dollars/acre) 4 5 Ewing 6 Bames 7 Pickens 8 9 Max % that can be sold to any bidder 10 11 Number of acres sold to bidders 12 13 Ewing 14 Bares 15 Pickens 16 Total 17 18 Available 19 20 Revenue ($millions) 21 22 23 24 25 26 28 29 30 31 32 al 33 C 34 35 36 37 38 39 40 Point X Retiremen nnin iont vrav A P5-43 fx | P5-46 COOOO 2000 1800 1900 135000 0 0 =SUM(B13:B15) 150000 B 1-SUMPRODUCT(B5:C7,B13:C15) P5-46 part B JUL 5 P5-52 Site 1 Site 1 B 1000 1500 1300 0.45 0 135000 0 + =SUM(C13:C15) 150000 C Site 2 Site 2 Geography =SUM(B13:C13) -SUM(B14:C14) =SUM(B15:C15) =B18+C18 D Set Objective: To: O Max Total N< $B$20 4 db Min By Changing Variable Cells: $B$13:$C$15 Sort <= <= KE Solver Parameters Subject to the Constraints: $B$16:$C$16 <= $F$13:$F$14 $D$13:$D$15 <= $B$18:$D$18 S E Filter Make Unconstrained Variables Non-Negative Select a Solving Method: Simplex LP Value Of: =$D$18*$C$9 =$D$18*$C$9 =$D$18*$C$9 л Reapply Advanced 0 F Max allowed Add Change Delete Reset All Load/Save Options Text to Columns 18 30 G ((( Wha Anal X DE
1 Jok A Oil lease auction 2 3 Bids for sites (dollars/acre) 4 5 Ewing 6 Bames 7 Pickens 8 9 Max % that can be sold to any bidder 10 11 Number of acres sold to bidders 12 13 Ewing 14 Bames 15 Pickens 16 Total 17 18 Available 19 20 Revenue ($millions) 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Point B P5-43 Site 1 $2,000 $1,800 $1,900 Site 1 135000 0 0 135000 $150,000 P5-46 $472,500,000 C Site 2 $1,000 $1,500 $1,300 0.45 Site 2 0 135000 0 135000 D P5-46 part B Total 135000 135000 0 $150,000 $300,000 E Specify the following information about the input to be varied and the outputs to be captured. Max allowed 135000 135000 135000 Parameters for oneway table Input cell: (Optional) Descriptive name for input: Values of input to use for table F $C$9 Maximum value: Increment: Base input values on following: Minimum value: Output cell(s): Land being auctioned $B$20 0.3 Use the values from the following range: Input value range: 0.9 0.05 Use the values below (separate with Input values: H OK Cancel Note about specifying output cells: The safest way to select multiple output cells or ranges is to put your finger on the Ctrl key and then drag as many output cell ranges as you like. This will automatically insert commas between the ranges you select. 1 J K L
Transcribed Image Text:1 Jok A Oil lease auction 2 3 Bids for sites (dollars/acre) 4 5 Ewing 6 Bames 7 Pickens 8 9 Max % that can be sold to any bidder 10 11 Number of acres sold to bidders 12 13 Ewing 14 Bames 15 Pickens 16 Total 17 18 Available 19 20 Revenue ($millions) 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Point B P5-43 Site 1 $2,000 $1,800 $1,900 Site 1 135000 0 0 135000 $150,000 P5-46 $472,500,000 C Site 2 $1,000 $1,500 $1,300 0.45 Site 2 0 135000 0 135000 D P5-46 part B Total 135000 135000 0 $150,000 $300,000 E Specify the following information about the input to be varied and the outputs to be captured. Max allowed 135000 135000 135000 Parameters for oneway table Input cell: (Optional) Descriptive name for input: Values of input to use for table F $C$9 Maximum value: Increment: Base input values on following: Minimum value: Output cell(s): Land being auctioned $B$20 0.3 Use the values from the following range: Input value range: 0.9 0.05 Use the values below (separate with Input values: H OK Cancel Note about specifying output cells: The safest way to select multiple output cells or ranges is to put your finger on the Ctrl key and then drag as many output cell ranges as you like. This will automatically insert commas between the ranges you select. 1 J K L
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