ប្រឡងពាក់កណ្ដាលឆមាស

library(mosaic)

## Registered S3 method overwritten by 'mosaic':
##   method                           from   
##   fortify.SpatialPolygonsDataFrame ggplot2

## 
## The 'mosaic' package masks several functions from core packages in order to add 
## additional features.  The original behavior of these functions should not be affected by this.

## 
## Attaching package: 'mosaic'

## The following objects are masked from 'package:dplyr':
## 
##     count, do, tally

## The following object is masked from 'package:Matrix':
## 
##     mean

## The following object is masked from 'package:ggplot2':
## 
##     stat

## The following objects are masked from 'package:stats':
## 
##     binom.test, cor, cor.test, cov, fivenum, IQR, median, prop.test,
##     quantile, sd, t.test, var

## The following objects are masked from 'package:base':
## 
##     max, mean, min, prod, range, sample, sum

library(mosaicCalc)

## 
## Attaching package: 'mosaicCalc'

## The following object is masked from 'package:stats':
## 
##     D

បំរេាប់

p <- function(q) {(10 + 0.5 * q)~q}
C <- function(q) {(100 + 10 * q + 0.5 * q^2)~q}

1. រកអនុគមន៍ចំណូល

R <- makeFun((10 + 0.5 * q) ~ q)
R

## function (q) 
## (10 + 0.5 * q)

2. រកអនុគមន៌ប្រាក់ចំណេ

P <- makeFun ((10 + 0.5 * q)-(100 + 10 * q + 0.5 * q^2)~q)
P

## function (q) 
## (10 + 0.5 * q) - (100 + 10 * q + 0.5 * q^2)

3. សង់ក្រាប

library(ggplot2)
q_vals <- seq(-10, 10, length.out = 100)
C_vals <- 100 + 10 * q_vals + 0.5 * q_vals^2
R_vals <- 10 + 0.5 * q_vals
df <- data.frame(q = q_vals, Cq = C_vals, Rq = R_vals)
ggplot(df, aes(x = q)) +
  geom_line(aes(y = Cq, color = "C(q)"), size = 1) +
  geom_line(aes(y = Rq, color = "R(q)"), size = 1) +
  geom_hline(yintercept = 0, linetype = "dashed", color = "gray") +
  geom_vline(xintercept = 0, linetype = "dashed", color = "gray") +
  labs(title = "Graphs of C(q) and R(q)", x = "q", y = "Function Values") +
  scale_color_manual(values = c("C(q)" = "blue", "R(q)" = "red")) +
  theme_minimal()

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

# 2. រកដេរីវេ C,R,P

C<- makeFun((100 + 10 * q + 0.5 * q^2) ~ q)
MC=D(C(q)~q)
MC

## function (q) 
## q + 10

MR= D(R(q)~q)
MR

## function (q) 
## 0.5

MP= D(P(q)~q)
MP

## function (q) 
## -(q + 9.5)

2.4 សង់ក្រាប

L_vals <- seq(0, 20, by = 0.1)
MP_vals <- MP(L_vals)
plot(L_vals, MP_vals, type = "l", col = "blue", lwd = 2,
     xlab = "L", ylab = "MP",
     main = " Marginal Product (MP)")

##3 ការបង្កើនប្រាក់ចំណេញអតិបរមា #3.1 ស្វែងរកបរិមាណ

library(Deriv)
R <- function(q) {
  (100 - 2 * q) * q
}
profit <- function(q) {
  R(q) - C(q)
}
profit_prime <- Deriv(profit)
q_optimal <- uniroot(function(q) profit_prime(q), c(0, 50))$root
q_optimal

## [1] 18

3.2 គណនាប្រាក់ចំណេញអតិបរមា

R <- function(q) {
  (100 - 2 * q) * q
}
C <- function(q) {
  50 + 20 * q + q^2
}
profit <- function(q) {
  R(q) - C(q)
}
profit_prime <- Deriv(profit)
q_optimal <- uniroot(function(q) profit_prime(q), c(0, 50))$root
q_optimal

## [1] 13.33333

4 ចំណុចស្រង់ដើម 4.1 ស្វែងរកបរិំមាណផលិត