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plz solve step by step clearly and show the formula Managers of an Auto Products company are considering the national launch of a new car

plz solve step by step clearly and show the formula

Managers of an Auto Products company are considering the national launch of a new car cleaning product. For simplicity, the potential average sales of the product during its lifetime are classified as being either high, medium, or low, and the net present value of the product under each of these conditions is estimated to be 80M, 15M, and -40M Tl respectively. The companys marketing manager estimates that there is a 0.3 probability that average sales will be high, a 0.4 probability that they will be medium. It can be assumed that companys objective is to maximize the net present value.

The managers have another option. Rather than going immediately for a full national launch, they could first test market the product. This would obviously delay the national launch, and this delay, together with other outlays would lead to costs having a net present value of 3M TL. The test marketing would give an indication as to the likely success of the national launch, and the realibility of each possible indications that could result are shown by the conditional probabilities are given below (e.g. f the market for the product is such that high sales could be achieved, there is a probability of 0.15 that the test marketing would in fact indicate medium sales):

Test marketing indication

Actual Sales

High

Medium

Low

High

0.80

0.15

0.05

Medium

0.25

0.60

0.15

Low

0.10

0.30

0.60

Determine whether the company should test market the product

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