install.packages("expm")
library(expm)
#جدول5
p00<- 0.65
p01<- 0.15
p10<- 0.15
cr<- 0.25
ca<- 2
cpm<-1
ccm<-10
p11<- 1-(p01+p10+p00)

pi <- c(0,0,1,0,0)
p <- matrix(c(0,0,0,0,1-p01-p11,
              0,0,0,1-p10-p11,0,
              p10,p01,p00,0,0,
              0,0,0,1-p10-p11,0,
              0,0,0,0,1-p01-p11),nrow=5,byrow=TRUE)
delta_c1 <- diag(c(0,1,1,1,0))
delta_c2 <- diag(c(1,0,1,0,1))


p_x1_N<- function(N,pi,p,delta_c1,delta_c2){
  e <- matrix(1,nrow=nrow(p),ncol=1)
  survival <- pi%*%diag(nrow(p))%*%delta_c2%*%(p%^%N)%*%delta_c1%*%e
  return(survival[1,1])
}

p_x2_N <- function(N,pi,p,delta_c1,delta_c2){
  e <- matrix(1,nrow=nrow(p),ncol=1)
  survival <- pi%*%diag(nrow(p))%*%delta_c1%*%(p%^%N)%*%delta_c2%*%e
  return(survival[1,1])
}



p_x1_x2_N <- function(N,pi,p,delta_c1,delta_c2){
  e <- matrix(1,nrow=nrow(p),ncol=1)
  survival <- pi%*%(p%^%N)%*%delta_c1%*% diag(nrow(p))%*%delta_c2%*%e
  return(survival[1,1])
}


E <- function(N,pi,p,delta_c1,delta_c2){
  sum <-0
  for(t in 0:(N-1)){
    sum <- sum +p_x1_N(t,pi,p,delta_c1,delta_c2)+p_x2_N(t,pi,p,delta_c1,delta_c2) -
      p_x1_x2_t(t,pi,p,delta_c1,delta_c2)
      
  }
  return(sum)
  
  }  
      
c_d_N <- function(N,pi,p,delta_c1,delta_c2,ccm,cpm,ca,cr){
  b_double_prime <- cpm-ccm-ca+cr
  
 
  numerator <- ccm+2*ca+b_double_prime*(p_x1_N(N,pi,p,delta_c1,delta_c2)+ p_x2_N(N,pi,p,delta_c1,delta_c2))
  -(cpm-ccm)*p_x1_x2_N(N,pi,p,delta_c1,delta_c2)
  
  denominator<- E(N,pi,p,delta_c1,delta_c2)
                                
  return(numerator/denominator)
}

C_d_values <- sapply(N_values,c_d_N,pi=pi,p=p,delta_c1=delta_c1,delta_c2=delta_c2
                     ,ccm=ccm,cpm=cpm,ca=ca,cr=cr)
results <- data.frame(N=N_values,c_d_N=C_d_values)

print(results)




#محاسبه ی تابع هزینه به ازای مقادیر داده شده
N_values<- 1:10
C_values<- sapply(N_values,C_d_values)

#پیدا کردن Nبهینه
optimal_N <- N_values[which.min(C_d_values)]
is_optimal <- TRUE
if(optimal_N >1 && optimal_N < length(N_values)){
  if(C_values[optimal_N] >= C_values[optimal_N-1] || C_values[optimal_N] >= C_values[optimal_N+1]){
    is_optimal <-FALSE
  }
}else{
  is_optimal <- FALSE
}

results<-data.frame(N=N_values,C_N=C_values)
print(results)

if(is_optimal){
  cat("Nبهینه :",optimal_N,"با هزینه :",C_values[optimal_N],"\n")
}else{
  cat("هیچNبهینه ای پیدا نشد که کمترین هزینه را نسبت به مقادیر قبلی و بعدی خود داشته باشد.\n")
}<pre>An Error occurred while handling another error:
yii\web\HeadersAlreadySentException: Headers already sent in  on line 0. in /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/Response.php:366
Stack trace:
#0 /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/Response.php(339): yii\web\Response-&gt;sendHeaders()
#1 /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/ErrorHandler.php(136): yii\web\Response-&gt;send()
#2 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/ErrorHandler.php(135): yii\web\ErrorHandler-&gt;renderException()
#3 [internal function]: yii\base\ErrorHandler-&gt;handleException()
#4 {main}
Previous exception:
yii\web\HeadersAlreadySentException: Headers already sent in  on line 0. in /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/Response.php:366
Stack trace:
#0 /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/Response.php(339): yii\web\Response-&gt;sendHeaders()
#1 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/Application.php(656): yii\web\Response-&gt;send()
#2 /var/www/html/prof-homepages/vendor/faravaghi/yii2-filemanager/models/Files.php(696): yii\base\Application-&gt;end()
#3 /var/www/html/prof-homepages/vendor/faravaghi/yii2-filemanager/controllers/FilesController.php(484): faravaghi\filemanager\models\Files-&gt;getFile()
#4 [internal function]: faravaghi\filemanager\controllers\FilesController-&gt;actionGetFile()
#5 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/InlineAction.php(57): call_user_func_array()
#6 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/Controller.php(180): yii\base\InlineAction-&gt;runWithParams()
#7 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/Module.php(528): yii\base\Controller-&gt;runAction()
#8 /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/Application.php(103): yii\base\Module-&gt;runAction()
#9 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/Application.php(386): yii\web\Application-&gt;handleRequest()
#10 /var/www/html/prof-homepages/frontend/web/index.php(18): yii\base\Application-&gt;run()
#11 {main}</pre>