z0=20
ro=0.3
landa=3
beta=1
c1=0.3 # hazine negahdari
c2=0.05 # hazine bazrasi
cr=10
B=10 # maximum of k
f <- function(x){
  lis <- list()
  for(i in 1:x) {
    lis[[i]] <-c(0,1)
  }
  do.call(expand.grid,lis)
}
L=function(M,tu){
p=pgamma( z0, landa^(tu), beta)-pgamma( M,  landa^(tu), beta)
q=1-pgamma( z0,  landa^(tu), beta)
for(j in 2:B) {
a=2^(j-1)
xx=f(j-1)
ppi=matrix(0,a,j-1)
ss1=c()
tt1=c()
for(i in 1:a) {
for(k in 1:(j-1))
{
if(xx[i,k]==1) ppi[i,k]=p[k]
if(xx[i,k]==0) ppi[i,k]=1-p[k]
}
x1=which(xx[i,]==1)
r=length(x1)
w=0
if(r>0) w=ro*x1[r]*tu
ss=(pgamma( z0,  landa^(j*tu-w), beta)-pgamma(M, landa^(j*tu-w), beta))*prod(ppi[i,])
ss1=c(ss1,ss)
tt=(1-pgamma( z0,  landa^(j*tu-w), beta))*prod(ppi[i,])
tt1=c(tt1,tt)
}
p=c(p,sum(ss1))
q=c(q,sum(tt1))
}

q=round(q,10)
BI=which.max(q)


q=q/sum(q[1:BI])
p=p/sum(p[1:BI])

E=function(k){
if(k==1) return(0) else return(sum(sapply(1 :(k-1),function(j) p[j])))
}

C=1+sum(sapply(1:BI,function(k)  (k*c2+c1*E(k))*q[k]))
TT=sum(sapply(1:BI ,function(k) k*tu*q[k]))
return(C*cr/TT)
}
L <- Vectorize(L,"M")
L <-Vectorize(L,"tu")
#L(c(20,30),c(0.3,0.4))

L1=function(M) L(M,tu)
tu=.5
optimize(L1, interval = c(0, z0))
<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>