Introduction To Operations Research By Frederick Hillier-Test Bank

Test Bank For Introduction To Operations Research By Frederick Hillier

Test Bank for Chapter 11

Drawback 11-1:

An organization is planning its promoting technique for subsequent yr for its three main merchandise. Because the three merchandise are fairly totally different, every promoting effort will deal with a single product. In items of tens of millions of {dollars}, a complete of 6 is out there for promoting subsequent yr, the place the promoting expenditure for every product have to be an integer higher than or equal to 1. The vice-president for advertising has established the target: Decide how a lot to spend on every product to be able to maximize complete gross sales. The next desk offers the estimated enhance in gross sales (in applicable items) for the totally different promoting expenditures.

Promoting Expenditure

Product

1 2 3

1

7 4 6

2

10 8 9

3

14 11 13

4

17 14 15

Use dynamic programming to unravel this drawback.

Answer for Drawback 11-1:

Because the choices to be made are the promoting expenditures on the three merchandise, the phases for a dynamic programming formulation of this drawback correspond to the three merchandise. When making the choice for a selected product, the important info is the quantity of the promoting funds nonetheless remaining, so this turns into the present state on this formulation.

Let xn be the promoting {dollars} (in tens of millions) spent on product n.

Let sn be the quantity of promoting funds remaining.

Let be the rise in gross sales of product n when xn million {dollars} are spent on product n, as given by the above desk.

Then, utilizing the same old dynamic programming notation introduced in Sec. 10.2 of the textbook, the recursive relationship for this drawback is

.

The answer process now begins on the finish (stage 3) and strikes backward stage by stage.

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