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# design a dynamic-programming solution that will help the theater manager go over the daily bids and select from among them the ones that will maximize the daily theater revenue R.

INSTRUCTIONS TO CANDIDATES

An exclusive all-day-long family theater has a capacity of C seats. To use the theater, each group must make a bid. Each bid cannot be less than a minimum amount (B) and any group can bid more than B to increase the chances of its bit being accepted to use the theater.

Your task is to design a dynamic-programming solution that will help the theater manager go over the daily bids and select from among them the ones that will maximize the daily theater revenue R.

1. (10 points) First, let's evaluate the following seemingly promising greedy

Evaluate the strategy of dividing the group bid amounts by the group sizes and picking the group with the largest amount per member first. Give an example to show that this strategy does not produce an optimal solution.

1. (10 points) Write an equation that expresses the maximum revenue R recursively and shows the optimal substructure of this
2. (10 points) Draw the recursion tree of the following Assume that the theater capacity (C) is 15 and the minimum bid amount (B) is also \$15

 Group 1 2 3 4 5 Group size 3 2 5 7 6 Group bid 30 15 40 60 50

1. (5 points) What is the optimal revenue (R) of the above example?
2. (5 points) How many possible solutions are there?
3. (10 points) Give a recursive solution to the recurrence equation of STEP
4. (15 points) Give a non-recursive bottom-up algorithm to calculate
5. (5 points) What is the running time of the STEP G algorithm?
6. (15 points) Give a recursive top-down memoized algorithm to calculate
7. (5 points) What is the running time of the STEP I algorithm?
8. (10 points) Give an algorithm for printing the numbers of the groups whose bids are
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