DATA_605_Discussion_13

** DATA_605_Discussion_13_Optimization_Chapter_4.3_Problem_3. **

** Optimization **

if (!require(Deriv)) install.packages("Deriv")

## Loading required package: Deriv

## Warning: package 'Deriv' was built under R version 3.3.3

library(Deriv)

if (!require(stats)) install.packages("stats")
library(stats)

Chapter 4.3

3). Find the maximum product of two numbers (not necessarily integers) that have a sum of 100.

Reference: see Example 102 in Chapter 4.3 of the calculus text(page 173)

# setup range to evalate the function (by testing)
max <- 2000
min <- -max


# setup equations:
# function:
# if
# a + b = 100
# then
# b = 100 - a
# and
# a * b = a * (100 - a)

funct_a <- function(a) {
    a * (100 - a)
}

# set derivative of function b
funct_a_der <- Deriv(funct_a)

# find root equation for derivative of b
root <- uniroot(funct_a_der, c(min, max))

#find the root
funct_a(root$root)

## [1] 2500

## [1] 2500

# plot the results
b <- seq(min, max)
plot(b, funct_a(b))
abline(root$root, root$f.root, col = "blue")

** END **

DATA_605_Discussion_13_DThonn