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A company's president believes that the time-cost tradeoff function for an innovation is C=200-60t+2t2. The company's...

A company's president believes that the time-cost tradeoff function for an innovation is C=200-60t+2t2. The company's president also believes that the present value of profit R=400-30t. What would be the optimal duration of the project?

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Answer #1

Profit (Z) = R - C

Z = (400 - 3t) - (200 - 60t + 2t2)

Z = 400 - 30t - 200 + 60t - 2t2

Z = 200 + 30t - 2t2

Duration is optimized when dZ/dt = 0.

dZ/dt = 30 - 4t = 0

4t = 30

t = 7.5

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