# Dynamic Programming Problem

A company is planning its advertising strategy for next year for its three major products. Since the three products are quite different, each advertising effort will focus on a single product. In units of millions of dollars, a total of 6 is available for advertising next year, where the advertising expenditure for each product must be an integer greater than or equal to 1. The vice-president for marketing has established the objective: Determine how much to spend on each product in order to maximize total sales. The following table gives the estimated increase in sales (in appropriate units) for the different advertising expenditures.

Advertising Expenditure Product

1 2 3

1 7 4 6

2 10 8 9

3 14 11 13

4 17 14 15

See attached file for full problem description.

Use dynamic programming to solve this problem.

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#### Solution Preview

Please see attached file.

Let's break the problem into three stages: each stage represents the money allocated to a single product. So stage 1 represents the money allocated to product 1, stage 2 the money to product 2, and stage 3 the money to product 3. We will artificially place an ordering on the stages, saying that we will first allocate to product 1, then product 2, then product 3.

Each stage is divided into states. A state encompasses the information required to go from one stage to the next. In this case the ...