In Wesvale, a small rural townin Maine, virtually all shopping and business is done in town. The town has onefarm and garden centerthat sells fertilizer to the local farmers and gardeners. The center carries three brands of fertilizer - Plant Plus, Crop Extra, and Gr0-Fast - so every person inthe town whousesfertilizer uses one of the three brands. The garden center has 9,000 customersforfertilizereach spring. An extensive market research study has determined that customers switch brands of fertilizers according to thefollowing probability transition matrix. This Spring Next Spring Crop Extra Plant Plus Gro-Fast Plant Plus .40 .30 .30 Crop Extra Gro-Fast .50 .10 .40 .40 .20 .40 The number of customers presently using each brand of fertilizer is shown in the followingtable. Fertilizer Brand Customers Plant Plus 3,000 Crop Extra Gro-Fast 4,000 2,000

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Author:David Poole
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Chapter2: Systems Of Linear Equations
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Solve using markov chain 1. Determine the steady state probabilities for the fertilizer brands
In Wesvale, a small rural townin Maine, virtually all shopping and business is done in
town. The town has onefarm and garden centerthat sellsfertilizer to the local farmers and
gardeners. The center carries three brands of fertilizer - Plant Plus, Crop Extra, and Gr0-Fast -
so every person inthetown who usesfertilizer uses one of the three brands. The garden center
has 9,000 customersforfertilizereach spring. An extensive market research study has
determined that customers switch brands of fertilizers according to thefollowing probability
transition matrix.
This Spring
Next Spring
Crop Extra
Plant Plus
Gro-Fast
Plant Plus
.40
.30
.30
Crop Extra
Gro-Fast
.50
.10
.40
,40
.20
.40
The number of customers presently using each brand of fertilizer is shownin the followingtable.
Fertilizer Brand
Customers
Plant Plus
3,000
Crop Extra
Gro-Fast
4,000
2,000
Transcribed Image Text:In Wesvale, a small rural townin Maine, virtually all shopping and business is done in town. The town has onefarm and garden centerthat sellsfertilizer to the local farmers and gardeners. The center carries three brands of fertilizer - Plant Plus, Crop Extra, and Gr0-Fast - so every person inthetown who usesfertilizer uses one of the three brands. The garden center has 9,000 customersforfertilizereach spring. An extensive market research study has determined that customers switch brands of fertilizers according to thefollowing probability transition matrix. This Spring Next Spring Crop Extra Plant Plus Gro-Fast Plant Plus .40 .30 .30 Crop Extra Gro-Fast .50 .10 .40 ,40 .20 .40 The number of customers presently using each brand of fertilizer is shownin the followingtable. Fertilizer Brand Customers Plant Plus 3,000 Crop Extra Gro-Fast 4,000 2,000
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