rm(list = ls())
library(distr)
T=360
B=1
c=0.05
L=900
MM=400
Cp=1
Ci=2
Cf=3
nmax=15

alpha=1
Target1=function(tau){

Pn_func=function(n){
  integrand=function(x){
   (1- pgamma(L-x,shape = alpha*tau,rate = B))*
      dgamma(x,shape = alpha*(n-1)*tau,rate = B)
  }
  p=integrate(integrand,lower = 0,upper = L)$value
  p
}
Pn_func=Vectorize(Pn_func,"n")

  n=1:nmax
  Pn=Pn_func(n)
  En=sum(n*Pn)
######################Enp######
Np_func=function(n){
  i=1:(n-1)
  Np=sum(
    pgamma(L,shape = alpha*i*tau,rate = B)-
      pgamma(MM,shape = alpha*i*tau,rate = B)
  )
  Np
}
Np_func=Vectorize(Np_func,"n")

  n=1:nmax
  Np=Np_func(n)
  #Pn=Pn_func(n, alpha, B, T, L)
  Enp=sum(Np*Pn)
 
#####################lL##############

   L=1000*(Cf+Ci*En+Cp*Enp)/(tau*En)
 
 return(L)

}
Target1=Vectorize(Target1,"tau")

optimize(Target1,c(1,3500))
plot(Target1,500,900,add=TRUE,type="l",lty=1,xlab=expression(tau),ylab=expression(eta(tau,alpha)))

alpha=1.3
Target1=function(tau){

Pn_func=function(n){
  integrand=function(x){
   (1- pgamma(L-x,shape = alpha*tau,rate = B))*
      dgamma(x,shape = alpha*(n-1)*tau,rate = B)
  }
  p=integrate(integrand,lower = 0,upper = L)$value
  p
}
Pn_func=Vectorize(Pn_func,"n")

  n=1:nmax
  Pn=Pn_func(n)
  En=sum(n*Pn)
######################Enp######
Np_func=function(n){
  i=1:(n-1)
  Np=sum(
    pgamma(L,shape = alpha*i*tau,rate = B)-
      pgamma(MM,shape = alpha*i*tau,rate = B)
  )
  Np
}
Np_func=Vectorize(Np_func,"n")

  n=1:nmax
  Np=Np_func(n)
  #Pn=Pn_func(n, alpha, B, T, L)
  Enp=sum(Np*Pn)
 
#####################lL##############

   L=1000*(Cf+Ci*En+Cp*Enp)/(tau*En)
 
 return(L)

}
Target1=Vectorize(Target1,"tau")

optimize(Target1,c(1,3500))
plot(Target1,500,900,add=TRUE,type="l",lwd=2,lty=2,xlab=expression(tau),ylab=expression(eta(tau,alpha)))

alpha=1.6
Target1=function(tau){

Pn_func=function(n){
  integrand=function(x){
   (1- pgamma(L-x,shape = alpha*tau,rate = B))*
      dgamma(x,shape = alpha*(n-1)*tau,rate = B)
  }
  p=integrate(integrand,lower = 0,upper = L)$value
  p
}
Pn_func=Vectorize(Pn_func,"n")

  n=1:nmax
  Pn=Pn_func(n)
  En=sum(n*Pn)
######################Enp######
Np_func=function(n){
  i=1:(n-1)
  Np=sum(
    pgamma(L,shape = alpha*i*tau,rate = B)-
      pgamma(MM,shape = alpha*i*tau,rate = B)
  )
  Np
}
Np_func=Vectorize(Np_func,"n")

  n=1:nmax
  Np=Np_func(n)
  #Pn=Pn_func(n, alpha, B, T, L)
  Enp=sum(Np*Pn)
 
#####################lL##############

   L=1000*(Cf+Ci*En+Cp*Enp)/(tau*En)
 
 return(L)

}
Target1=Vectorize(Target1,"tau")

optimize(Target1,c(1,3500))
plot(Target1,500,900,add=TRUE,type="l",lwd=2,lty=3,xlab=expression(tau),ylab=expression(eta(tau,alpha)))
legend("topright",c(expression("alpha=1"),expression("alpha=1.3"),expression("alpha=1.6")),lty=c(1,2,3))









<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>