$3.)$ Solve using Wagner Whitin $($Dynamic Programming $-$ Operations Research$)$

$*$Use backward recursion$3.)$ Solve using

Wagner Whitin

$($Dynamic

Programming $-$

Operations

Research$)$

$*$use backward

recursion

EXAMPLE ONLY

Automobile Replacement.

Suppose you would like to minimize your automobile transportation costs over the next five

years. Let us assume that presently you do not own a car and that over the next four years you

will consider buying new cars only at the start of each year. The average price of a new car over

the next four years is expected to be $$5,000.$ You decide that you would not keep a car longer

than three years. The table below gives the operating costs and trade$-$in values for each type of

car. There is no requirement that you dispose of your car at the end of the fifth year. Your

objective is to minimize purchase plus operating costs during years $1-5.$ Use DP to determine the

optimal policy.