evaluating function over seq of values

The MWE (below) shows what I'm hoping to get some help with:

step 1\ specify the likelihood expression I want to evaluate using a
brute-force grid search (not that I would do this in practice, but it is a
convenient approach to explain the idea in a class...).

step 2\ want to evaluate the likelihood at each of a sequence of values of N
(for this example, seq(80,200,1)).

step 3\ take all of the values of the likelihood at each value for N, and
(say) plot them

I'm sure there is a clever way to vectorize all this, but my token attempts
at wrestling sapply into submission have failed me here. In my MWE, I use a
simple loop, which has the advantages of working, and being completely
transparent as to what it is doing. For teaching purposes, this is perhaps
fine, but I'm curious as to how I could accomplish the same thing avoiding
the loop.

Thanks in advance...

-----<MWE code below>-----


# ML estimation by simple grid search

rm(list=ls())
library("optimx")

# set up likelihood function

f_like <- function(par) {
                            p1 <- par[1];
                            p2 <- par[2];
                            p3 <- par[3];
                            p4 <- par[4];
                                   lfactorial(N)-lfactorial(N-79) +
                                    (30*log(p1)+(N-30)*log(1-p1)) +
                                    (15*log(p2)+(N-15)*log(1-p2)) +
                                    (22*log(p3)+(N-22)*log(1-p3)) +
                                    (45*log(p4)+(N-45)*log(1-p4)) }


# do the otimization using optimx nested in a loop (works, but guessing
there is an
# easier way using lapply or some such...)

count <- 1;

dat <- matrix(c(0,0,0),length(seq(80,200,1)),3)

for (N in seq(80,200,1)) {

results_optx <- optim(c(0.2,0.2,0.2,0.2), f_like,
     method = "L-BFGS-B", lower=c(0.005,0.005,0.005,0.005),
upper=c(0.990,0.995,0.995,0.995),
      hessian = TRUE,control=list(fnscale=-1))

like_mod <- results_optx$value;
 dat[count,1] <- count;
 dat[count,2] <- N;
 dat[count,3] <- like_mod;
count=count+1;
}

plot(dat[,2],dat[,3],type="l",bty="n",  xlim=c(79,205), yaxs =
"i",main="likelihood profile",xlab="N", ylab="Likelihood")