Question

A manufacturer must decide whether to institute, at a cost of

$75,000, a new advertising campaign. It is estimated that, if the

campaign is very successful, profit will increase by $300,000

(excluding the cost of the advertising campaign). If the campaign is

moderately successful, profit will increase by $120,000, while, if the

campaign is unsuccessful, profit will remain unchanged. It is

estimated that the probabilities for very successful, moderately

successful, and unsuccessful advertising campaigns are 0.2, 0.5, and 0.3, respectively.

1. Set up the payoff table

2. If the expected monetary value criterion is used, should the advertising

campaign be instituted?

3. Use the most likely event criterion to find the best action.

4. Use the expected regret criterion to choose the best action.

5. Draw the manufacturer’s decision tree.

Answer 1

1. Payoff table

Payoff when advertising is applied for each scenario= profit increase in that scenario- cost of advertizing

	Highly successful	Moderately successful	Unsuccessful
Invest in advertising	225000	45000	-75000
Not invest in advertising	0	0	0

2. Expected money criteria

Expected payoff if invested in advertising= probability of highly successful* payoff of highly succesful+probability of moderately successful* payoff of moderately succesful+probability of unsuccessful* payoff of unsuccessful = 0.2*225000+0.5*45000+0.3*(-75000)=45000

The expected payoff if not invested=0

3. most likely event criterion to find the best action

Most likely event if invested is that advertizing in moderately successful and thus the payoff is 45000 and the most likely scenario if not invested in not investing is all 3 which have payoff of0. Hence we would invest in advertising.

4.

	Highly successful	Moderately successful	Unsuccessful
Invest in advertising	225000	45000	-75000
Not invest in advertising	0	0	0
	Highly successful	Moderately successful	Unsuccessful
The maximum payoff in each scenario	225000	45000	0
Regret=Maximum payoff-Situation payoff
Maximum payoff- situation payoff	Highly successful	Moderately successful	Unsuccessful	Maximum regret
Invest in advertising	0	0	75000	75000
Not invest in advertising	225000	45000	0	225000

As we can see minimum of maximum regret happens in Situation 1 when invested in advertising, hence we would invest in advertizing