A company that produces passenger cars reviews the annual sales and lassifies it in one of 2 states: 0 (unsuccessful, sales are low) and 1 (successful, sales are igh). The marketing manager then decides on whether or not to advertise this car to urther promote the sales. The “no advertisement" decision is label as k =1 and the advertisement" decision is k = 2. Past data indicates that that the transition probabilities or each decision is given below: [0.9 0.1 0.31 „P(2) = l0.2 [0.7 P,(1) = 06 0.4) 0.8 lo.6 0.4] 0.8] Moreover, the annual "pro fit" matrix if decision k is taken when the state is i is estimated IS -31 Cik 30 25 The marketing manager wants to find the optimal policy in order to maximize the average profit per year.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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A company that produces passenger cars reviews the annual sales and
classifies it in one of 2 states: 0 (unsuccessful, sales are low) and 1 (successful, sales are
high). The marketing manager then decides on whether or not to advertise this car to
further promote the sales. The “no advertisement" decision is label as k =1 and the
"advertisement" decision is k = 2. Past data indicates that that the transition probabilities
for each decision is given below:
0.7
0.6 0.4) P,(2) = [2 08
Moreover, the annual "profit" matrix if decision k is taken when the state is i is estimated
as
9-
-3°
Cik
30
25.
The marketing manager wants to find the optimal policy in order to maximize the average
profit per year.
a)
at all in any state.
What is the average profit per year if the manager chooses not to advertise
b)
optimal policy (do not solve it),
Determine the primal linear programming formulation in order to find the
c)
that the initial policy is not to advertise at all in any state.
Perform only 1 iteration of the policy improvement algorithm assuming
Transcribed Image Text:A company that produces passenger cars reviews the annual sales and classifies it in one of 2 states: 0 (unsuccessful, sales are low) and 1 (successful, sales are high). The marketing manager then decides on whether or not to advertise this car to further promote the sales. The “no advertisement" decision is label as k =1 and the "advertisement" decision is k = 2. Past data indicates that that the transition probabilities for each decision is given below: 0.7 0.6 0.4) P,(2) = [2 08 Moreover, the annual "profit" matrix if decision k is taken when the state is i is estimated as 9- -3° Cik 30 25. The marketing manager wants to find the optimal policy in order to maximize the average profit per year. a) at all in any state. What is the average profit per year if the manager chooses not to advertise b) optimal policy (do not solve it), Determine the primal linear programming formulation in order to find the c) that the initial policy is not to advertise at all in any state. Perform only 1 iteration of the policy improvement algorithm assuming
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