# Question: A real estate development firm Peterson and Johnson is considering

A real estate development firm, Peterson and Johnson, is considering five possible development projects. The following table shows the estimated long-run profit (net present value) that each project would generate, as well as the amount of investment required to undertake the project, in units of millions of dollars.

The owners of the firm, Dave Peterson and Ron Johnson, have raised $20 million of investment capital for these projects. Dave and Ron now want to select the combination of projects that will maximize their total estimated long-run profit (net present value) without investing more that $20 million.

(a) Formulate a BIP model for this problem.

(b) Display this model on an Excel spreadsheet.

(c) Use the computer to solve this model.

The owners of the firm, Dave Peterson and Ron Johnson, have raised $20 million of investment capital for these projects. Dave and Ron now want to select the combination of projects that will maximize their total estimated long-run profit (net present value) without investing more that $20 million.

(a) Formulate a BIP model for this problem.

(b) Display this model on an Excel spreadsheet.

(c) Use the computer to solve this model.

## Relevant Questions

Use the BIP branch-and-bound algorithm presented in Sec. 12.6 to solve the following problem interactively: Minimize Z = 5x1 + 6x2 + 7x3 + 8x4 + 9x5, Subject to and xj is binary, for j = 1, 2, . . . , 5. Five jobs need to be done on a certain machine. However, the setup time for each job depends upon which job immediately preceded it, as shown by the following table: The objective is to schedule the sequence of jobs that ...Reconsider the IP model of Prob. 12.5-2. (a) Use the MIP branch-and-bound algorithm presented in Sec. 12.7 to solve this problem by hand. For each subproblem, solve its LP relaxation graphically. (b) Now use the interactive ...For each of the following constraints of pure BIP problems, use the constraint to fix as many variables as possible: (a) 20x1 – 7x2 + 5x3 ≤ 10 (b) 10x1 – 7x2 + 5x3 ≥ 10 (c) 10x1 – 7x2 + 5x3 ≤ –1 One of the constraints of a certain pure BIP problem is 3x1 + 4x2 + 2x3 + 5x4 ≤ 7. Identify all the minimal covers for this constraint, and then give the corresponding cutting planes.Post your question