Question

10. A manager is responsible for n machines. In any given period, the probability that exactly k machines will break down is Tk> 0 (πΟΤ π1+π2+ π,-1), where k is any whole number between 0 and n: k=0, 1, 2, , n. The Tk are "true" probabilities but are known only to the manager. The manager must report these probabilities to the control authority. In the absence of any re ward or penalty, he might report some wrong probabilities Po, Pi, ..., P (Po+P+P-1) The central authority devises the following scheme: if k machines break down, and the reported probability is P, the authority will pay the manager A +M In Pk dollars, where M and A are positive constants. The manager's expected reward is therefore The manager wants to choose Po,..., P, to maximize (1), subject to the con- straints that (a) Find the first-order conditions (ignore nonnegativity restrictions) (b) Are the second-order conditions satisfied? (c) Show that it is optimal for the manager to report the truth, i.e., Pi- TK-

Answer 1

#include <iostream>
#include <iomanip>
#include <cstdlib>
#include <string>
#include <unistd.h>//library for sleep

using std::cin;
using std::cout;
using std::endl;
using std::setw;
using std::setfill;//used to make 5-digit ID's
using std::string;

class Student//class required to store the user's ID, name and time spent on the computer.
{
private:
//needed variables..kept private
int time;
int ID;
string Name;
public:
//setters & getters
void setName(string);
string getName();
void setID(int);
int getID();
void setTime(int);
int getTime();
Student();//constructor
~Student();//deconstructor
};

//deconstructor for the class Student, empty braces
Student::~Student(){}

Student::Student()//just gives initial values to the three private variables of the class
{
ID = -1;//will store the random ID
Name = "";//stores the valid string from user
time = 0;//stores the time desired by user
}

//Pre: just needs to be called with a string type parameter
//Post: nothing returned but Name gets the parameter x
void Student::setName(string x)
{
Name = x;
}

//Pre: needs to be called with dot operator
//Post: returns the value in Name (string)
string Student::getName()
{
return Name;
}

//Pre: needs to be called and have an int parameter
//Post: nothing returned but ID gets the parameter y
void Student::setID(int y)
{
ID = y;
}

//Pre: needs called by . operator
//Post: returns the value in ID as an int
int Student::getID()
{
return ID;
}

//Pre: needs to be called and have an int parameter
//Post: nothing returned but time gets the parameter z
void Student::setTime(int z)
{
time = z;
}