1) Solve LCS problem using dynamic programming:
algorithms
agronomy

2) Solve using simplex method:
x,y >= 0
3x + 3y <= 420
x  + 4y <= 440
x       <= 80
f(x,y) = 60x + 30y -> MAX

3) Design greedy procedure for the following problem -- interval coloring: you
have a list of classes that specifies class start and end time [s_i,e_i].  You
have to assign rooms to classes -- your goal is to minimize the total number of
rooms used. Obviously you cannot skip a class and if two classes overlap they
cannot be in the same room. The problem can be stated as color given intervals
in fewest number of colors, so that no two intervals with the same color
overlap.

4) Design recursive formula (first step in designing DP algorithm) for the 
problem:
How many n-digit numbers have exactly k bits set?

5) You are given a collection if n bolts of different width and n
corresponding nuts. You are allowed to try a nut and a bolt together, from
which you can determine whether the nut is larger than the bolt, smaller
than the bolt, or matches the bolt exactly.  However, there is no way to
compare two bolts together, or two nuts together. The problem is to match
each bolt to its nut.  Design an algorithm for this problem with
average-case efficiency in Theta( n log n ).

6) You need to buy some filing cabinets. You know that Cabinet X costs $10 per
unit, requires six square feet of floor space, and holds eight cubic feet of
files. Cabinet Y costs $20 per unit, requires eight square feet of floor space,
and holds twelve cubic feet of files. You have been given $140 for this
purchase, though you don't have to spend that much. The office has room for no
more than 72 square feet of cabinets. How many of which model should you buy,
in order to maximize storage volume?
Convert to a linear programming problem - DO NOT SOLVE THE LPP.

7) Given two strings a and b, the edit distance d(a, b) is the
minimum-weight series of edit operations that transforms a into b.

Allowed operations (all 3 have the same cost - say 1): 
Insertion of a single symbol at any position
Deletion of a single symbol changes at any position
Substitution of a single symbol at any position

Design DP solution to find edit distance.

8) Surprise

9) Surprise