A television station would like to decide between extending a current television show for another season or develop a completely new show for that time slot.

It will cost $6M to develop the new show. The new show may be very successful, moderately successful, or not successful with associated advertising revenues of $25M, $15M, or $5M, respectively.

If the station chooses to extend the current show, it will cost $2M. The extended show may be very successful, moderately successful, or not successful with associated advertising revenues of $15M, $10M, or $5M, respectively.

The probabilities associated with the very successful, moderately successful, and not successful new show are 0.2, 0.5, and 0.3, respectively. The probabilities associated with very successful, moderately successful, and not successful existing show are 0.3, 0.4, and 0.3, respectively.

Which of the following are true at the television station's decision problem?

Question

A television station would like to decide between extending a current television show for another season or develop a completely new show for that time slot.

It will cost $6M to develop the new show.  The new show may be very successful, moderately successful, or not successful with associated advertising revenues of $25M, $15M, or $5M, respectively.

If the station chooses to extend the current show, it will cost $2M.  The extended show may be very successful, moderately successful, or not successful with associated advertising revenues of $15M, $10M, or $5M, respectively.

The probabilities associated with the very successful, moderately successful, and not successful new show are 0.2, 0.5, and 0.3, respectively.  The probabilities associated with very successful, moderately successful, and not successful existing show are 0.3, 0.4, and 0.3, respectively.

Which of the following are true at the television station's decision problem?

BlackTom AI · Accepted Answer

We start by parsing the decision problem and computing the expected monetary value (EMV) for each option by considering profits (revenues minus development/extension costs) and their probabilities.
Option 1: The expected value of the new show decision is $8.5M.
- New show costs 6M to develop. Revenues: 25M (prob 0.2), 15M (0.5), 5M (0.3).
- Profit outcomes are: 25-6 = 19; 15-6 = 9; 5-6 = -1.
- EMV = 0.2*19 + 0.5*9 + 0.3*(-1) = 3.8 + 4.5 - 0.3 = 7.999 ≈ 8.0M, not 8.5M. This statement is false.

Option 2: The expected value of extending the current show decision is $8.0M.
- Extend costs 2M. Revenues: 15M (0.3), 10M (0.4), 5M (0.3).
- Profit outcomes are: 15-2 = 13; 10-2 = 8; 5-2 = 3.
- EMV = 0.3*13 + 0.4*8 + 0.3*3 = 3.9 + 3.2 + 0.9 = 8.0M. This statement is true.

Option 3: Based on the EMV, the unique best decision to develop the new show.
- We found EMV(New) ≈ 8.0M and EMV(Extend) = 8.0M. They are equal, not uniquely higher for the new show.
- Therefore there is no unique best decision to develop the new show; the best EMV is tied between the two options. This statement is false.

Option 4: The EMV of the decision tree is $8.0M.
- The decision tree would compare the two options; since both yield an EMV of 8.0M, the EMV of the best decision (or the tree’s overall EMV) is 8.0M.
- This statement is true.

Option 5: Exactly two answers are correct.
- From the analyses: Option 2 is true and Option 4 is true; Options 1, 3 are false, and Option 5 (Exactly two answers are correct) is therefore true because there are exactly two true statements among these options. This statement is true.

Option 6: None of the answers are correct.
- Since we identified true statements (Options 2, 4, and 5), this blanket claim is false.

Summary of truth values:
- Option 1: false
- Option 2: true
- Option 3: false
- Option 4: true
- Option 5: true
- Option 6: false

Therefore, the true statements are that the EMV for extending is $8.0M, the EMV for the new show is $8.0M, and exactly two answers are correct (Options 2, 4, and 5 align with that).

MGMT 101 LEC ONL: MANA... Study Checkpoint 8: Decision Analysis I

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