Question $1(20$ points$)$

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

following tahle gives the estimated amount of sales for each product $($in apprepriate units$)$ for the

different advertising expenditures:

Use dynamic programming to determine how much to spend on each product in order to

maximize total sales. Write the stage, state, decision, recursive relationship and optimal solution

clearly.

Stage: Each product $($tin$\{1,2,3\})$s$\_($t$)($x$\_($t$))$