Dynamic Optmization

Question

I'm trying to set a problem that maximizes the consumption(u) over the time (10 years) subject to the variation of wealth (x_t+1 - x_t= -c_t), where x₀=1000. I've tried to solve it, but can't evaluate function at initial parameters. Also, the final conditions are: x₁₀ >= 0 and u₁₀ >= 0. Here's the code I'm using:

library('optimx')

# Parameters
t <- seq(0,10) # time
desc <- 0.1 # tax
beta <- 1/(1+desc) # parameter of function
alpha <- 0.8 # function
xo = 1000 # wealth in t=0

# Variables
x <- rep(xo, length(t)) # wealth in time

# Function
utilidade_total <- function(u, npar=TRUE, print=TRUE){
  for (i in lenght(t)){
    obj[i]=(beta^i)*(u[i]^alpha)
    x[i]=x[i-1]-u[i-1]
  }
  result <- sum(obj)
  return(result)
}

maxuti <- optimx(par=u,fn= utilidade_total,
                 control = list(maximize=TRUE))

umax <- coef(maxuti)

for (i in 2:lenght(t)){
   print(obj[i]=(beta^i)*(u^alpha))
    print(stock[i]=x[i-1]-umax[i-1])
}

# Result
for (i in 2:lenght(t)){
  obj[i]=(beta^i)*(u^alpha)
  x[i]=x[i-1]-u[i-1]
}

plot(t, x, type='b')
plot(t, u, type='b')