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B. No.
Cash Cow = low growth and high market share.
Dogs = low growth and low market share.
The answer is NO, because your cash cow is anyways doing so well and why would you want to take out your capital from there and invest in a problem child which might get extinct from the market as the reason of its low market share and growth. It also falls under the dog section in the BCG Matrix.
I agree with all of you on "NO", as I want exhaust my cash cow for the problem child that may be disposed by the market due to its low market share. However, there are some companies who may do that, just to their name in the market for some strategic reasons.
B. NO
A problem child has the potential to turn it into a dog.