A Company Is Planning Its Advertising Strategy for Next Year

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The Answer is Since the decisions to be made are the advertising expenditures on the three products,the stages for a dynamic programming formulation of this problem correspond to the three products.When making the decision for a particular product,the essential information is the amount of the advertising budget still remaining,so this becomes the current state in this formulation.Let x_n be the advertising dollars (in millions)spent on product n.Let s_n be the amount of advertising budget remaining.Let

Since the decisions to be made are the advertising expenditures on the three products,the stages for a dynamic programming formulation of this problem correspond to the three products.When making the decision for a particular product,the essential information is the amount of the advertising budget still remaining,so this becomes the current state in this formulation.Let x<sub>n</sub> be the advertising dollars (in millions)spent on product n.Let s<sub>n</sub> be the amount of advertising budget remaining.Let be the increase in sales of product n when x<sub>n</sub> million dollars are spent on product n,as given by the above table.Then,using the usual dynamic programming notation presented in Sec.10.2 of the textbook,the recursive relationship for this problem is .The solution procedure now starts at the end (stage 3)and moves backward stage by stage.For n = 3, For n = 2, For n = 1, Hence,since s<sub>2</sub> = 6 - and s<sub>3</sub> = s<sub>2</sub> - ,there are two optimal plans as given in the table below.

be the increase in sales of product n when x_n million dollars are spent on product n,as given by the above table.Then,using the usual dynamic programming notation presented in Sec.10.2 of the textbook,the recursive relationship for this problem is

.The solution procedure now starts at the end (stage 3)and moves backward stage by stage.For n = 3,

For n = 2,

For n = 1,

Hence,since s₂ = 6 -

and s₃ = s₂ -

,there are two optimal plans as given in the table below.

A Company Is Planning Its Advertising Strategy for Next Year

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