The SoftDrink Company must decide whether or not to introduce a new diet drink. Management feels that if it does introduce the diet soda it will yield a profit of $1 million if sales are around 100 million, a profit of $200,000 if sales are around 50 million, or it will lose $2 million if sales are only around 1 million bottles. If the company does not market the new diet soda, it will suffer a loss of $400,000. An internal marketing research study has found P(100 million in sales) = 1/3; P(50 million in sales) = 1/2; P(1 million in sales) = 1/6. ShouldSoftDrink introduce the new diet soda?

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hungqp96 hungqp96 · Answer 1 · 2019-10-25T05:02:23+02:00

Answer: SoftDrink should introduce the new diet soda.

Step-by-step explanation:

Denote:

[tex]P_1 = P(Sales = 100.000.000) = \frac{1}{3}; \pi_1 = 100,000,000[/tex]

[tex]P_2 = P(Sales = 50,000,000) = \frac{1}{2}; \pi_2 = 200,000[/tex]

[tex]P_3 = P(Sales = 1,000,000) = \frac{1}{6}; \pi_2 = -2,000,000[/tex]

whereby [tex]P_i, \pi_i[/tex] are the probability of occurence and the corresponding profit for each scenario.

As such, the expected profit can be calculated as follows:

[tex]E(\pi)=\sum_{i=1}^{3}P_i\pi_i = P_1\pi_1 + P_2\pi_2 + P_3\pi_3 = 100,000[/tex]

The new product is expected to make a profit, therefore, it should be introduced.