Introduction To Operations Research By Frederick Hillier-Test Bank

Exam Resource For Introduction To Operational Research By Frederick Hillier

Exam resource for Chapter 11

Disadvantage 11-1:
An enterprise is strategizing its marketing approach for the upcoming year for its three primary commodities. Since the three items differ significantly, each marketing effort will concentrate on a single product. In units of millions of bucks, a total of 6 is allocated for marketing next year, where the marketing expenditure for each product must be an integer greater than or equal to 1. The marketing vice president has set the objective: Determine the optimal expenditure on each product to maximize total sales. The subsequent table presents the projected sales increase (in appropriate units) for the different marketing expenditures.

Marketing Expenditure

Product

1 2 3

1

7 4 6

2

10 8 9

3

14 11 13

4

17 14 15

Utilize progressive programming to address this issue.

Resolution for Disadvantage 11-1:
Since the determinations to be made are the marketing expenses on the three products, the phases for a dynamic programming representation of this issue correspond to the three products. While deciding for a particular product, the key information is the amount of the remaining marketing budget, which becomes the current state in this representation.

Assume xn represents the marketing funds (in millions) spent on product n.

Assume sn represents the amount of remaining marketing budget.

Let be the sales increase of product n when xn million dollars are spent on product n, as detailed in the above table.

Thus, employing the typical dynamic programming symbols introduced in Sec. 10.2 of the textbook, the recursive relationship for this issue is

.

The resolution procedure now commences at the conclusion (level 3) and advances backward level by level.

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