The rod-cutting problem exhibits optimal substructure - that is, the optimal solution to maximizing revenue for cutting a rod of length n incorporates the optimal solution to some subproblems of cutting a rod of length less than n. (note that this allows the possibility that the optimal solution may not involve cutting the rod at all).

a. True
b. False

It is right to cut a rod into pieces to maximize revenue

when a rod is cut then rod lengths are an integral number of inches

Let's suppose length n and table of prices for i = 1,2,.......,n is given input and the maximum revenue for rods whose sum to n. If p is large, then the optimal solution requires no cuts.

Explanation:

Lets suppose possible cuts length and price

length i  = 1 2 3 4 5 6 7 8 9 10

price p   = 1 5 8 9 10 17 17 20 24 30

i       r        optimal solution

1      1          no cuts

2      5         no cuts

3     8          no cuts

4     10        2+2

5     13         2+3

6    17           no cuts

7      18        1+ 6

8       22       2+ 6

Optimal revenue in shorter rods :

After making a cut we have sub problems

For example, n= nine optimal solutions cut 2 inches; there are two sub problems of lengths two, and 7.there is a need to save both optimal. The optimal solution for the problem of length 2 is no cut and optimal solution for length seven is cut into length 5 and 2 then 2 is no cut then the optimal solution for length five is cut into length 2 and 3 then price will be 5$ + 5$ + 5$  + 8$ = 23$

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