An entrepreneur with $8 million to invest is considering acquisition of four companies. She estimates the cost of acquiring the four at $5, $1, $2, and $7 million, respectively, and the present value of owning them at $8, $3, $4, and $10. Investments are on an "all or nothing" basis (i.e., she must buy entire companies). Model as a dynamic program the problem of deciding which investments she should choose. a) Formulate the entreprenur's problem as an Integer Knapsack model. b) Define the states and stages of the corresponding discrete dynamic program to compute an optimum. c) Draw the digraph corresponding to your model of (b). d) Solve the model of (a) by identifying an optimal path in the figure of (c).
An entrepreneur with $8 million to invest is considering acquisition of four companies. She estimates the cost of acquiring the four at $5, $1, $2, and $7 million, respectively, and the present value of owning them at $8, $3, $4, and $10. Investments are on an "all or nothing" basis (i.e., she must buy entire companies). Model as a dynamic program the problem of deciding which investments she should choose. a) Formulate the entreprenur's problem as an Integer Knapsack model. b) Define the states and stages of the corresponding discrete dynamic program to compute an optimum. c) Draw the digraph corresponding to your model of (b). d) Solve the model of (a) by identifying an optimal path in the figure of (c).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:An entrepreneur with $8 million to invest is
considering acquisition of four companies. She
estimates the cost of acquiring the four at $5, $1, $2,
and $7 million, respectively, and the present value of
owning them at $8, $3, $4, and $10. Investments are
on an "all or nothing" basis (i.e., she must buy entire
companies). Model as a dynamic program the
problem of deciding which investments she should
choose.
a) Formulate the entreprenur's problem as an
Integer Knapsack model.
b) Define the states and stages of the corresponding
discrete dynamic program to compute an
optimum.
c) Draw the digraph corresponding to your model of
(b).
d) Solve the model of (a) by identifying an optimal
path in the figure of (c).
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