Assume that there are certain types of investment projects that can increase your money. Let's assume that project i need investment a; to be done. Once the project is established, it returns your initial investment and gives you an additional profit b₁. Each project may be established once. Currently you have an amount of money equal p. Note that you can't establish a project that takes more money than what you currently have. Your task is to find the maximum possible profit out of these projects. Input The first line contains the integers n and p, where n is the number of available projects and p is your initial amount of money. Then two lines follow, each containing n integers describing the arrays a and b [Note: a; the amount of money that you have to invest (spend) to establish the project i. b;: the amount of revenue that you get as an addition to the amount of money already spent to establish the project i. Output For each test case, output a single value that present the maximum profit you can achieve. Example Ex1 np a₁ →→ b; → Ex2 np a; → b; → Ex3 np a; → b; → input 5 $200 $200 $200 $500 $200 $200 $200 $200 $200 $200 $200 3 $150 $200 $400 $150 $90 $1000 $50 5 $80 $1280 $640 $320 $160 $80 $1280 $640 $320 $160 $80 output $1000 $140 $2480
Assume that there are certain types of investment projects that can increase your money. Let's assume that project i need investment a; to be done. Once the project is established, it returns your initial investment and gives you an additional profit b₁. Each project may be established once. Currently you have an amount of money equal p. Note that you can't establish a project that takes more money than what you currently have. Your task is to find the maximum possible profit out of these projects. Input The first line contains the integers n and p, where n is the number of available projects and p is your initial amount of money. Then two lines follow, each containing n integers describing the arrays a and b [Note: a; the amount of money that you have to invest (spend) to establish the project i. b;: the amount of revenue that you get as an addition to the amount of money already spent to establish the project i. Output For each test case, output a single value that present the maximum profit you can achieve. Example Ex1 np a₁ →→ b; → Ex2 np a; → b; → Ex3 np a; → b; → input 5 $200 $200 $200 $500 $200 $200 $200 $200 $200 $200 $200 3 $150 $200 $400 $150 $90 $1000 $50 5 $80 $1280 $640 $320 $160 $80 $1280 $640 $320 $160 $80 output $1000 $140 $2480
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter11: Nonlinear Programming
Section11.13: Pareto Optimality And Tradeoff Curves
Problem 5P
Related questions
Question
can you solve this on python please ?
a) Design a brute-force
b) Design a more efficient algorithm to do the same task with less complexity and analyse the complexity of your solution. [Important instruction to be followed: Create an arbitrary input of at least 5 projects and use it to provide full explanation of how your proposed algorithm should work step by step]
c) Develop a python code to implement your efficient algorithm.
and can you please compare between the algorithms
Transcribed Image Text:Assume that there are certain types of investment projects that can increase your money.
Let's assume that project i need investment a, to be done. Once the project is established,
it returns your initial investment and gives you an additional profit b₁. Each project may be
established once. Currently you have an amount of money equal p. Note that you can't
establish a project that takes more money than what you currently have. Your task is to
find the maximum possible profit out of these projects.
Input
The first line contains the integers n and p, where n is the number of available projects
and p is your initial amount of money.
Then two lines follow, each containing n integers describing the arrays a and b
[Note:
a: the amount of money that you have to invest (spend) to establish the project i.
b;: the amount of revenue that you get as an addition to the amount of money already
spent to establish the project i.
Output
For each test case, output a single value that present the maximum profit you can
achieve.
Example
Ex1
Ex2
Ex3
np
a; →
b; →
np
a; →
b; →
np
a; →
b; →
input
5 $200
$200 $200 $500 $200 $200
$200 $200 $200 $200 $200
3 $150
$200 $400 $150
$90 $1000 $50
5 $80
$1280 $640 $320 $160 $80
$1280 $640 $320 $160 $80
output
$1000
$140
$2480
Explanation
In the first example, your initial amount of money is $200, which enable you to invest in
the first, second, fourth and fifth project that needs only $200 each. By establishing these
four projects apart, the investor will have $200*4 (profit) +$200 (initial basic) = $1000. This
amount of money will enable the establishment the 3rd project that needs $500 of
investment to gain $200 of profit. Finally, to calculate the overall profit, you have collected
$1200, where $200 of them are the initial basic and hence the profit is $1200 - $200 =
$1000.
In the second example, your initial amount of money is $150, which enable you to invest
in the 3rd project only. By doing so, your budget will increases to $200 and hence be able
to invest in the 1st project to again increase your budget to $290. However, this is not
enough to invest in the 3rd project. Finally, you collected $290, where $150 of them are
the initial basic and hence the profit is $290 - $150 = $140.
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