Maximization problem

[schnappifx]

 

[stapel]

View attachment 8455

Your sideways image is difficult to read. I think the exercise is along the following lines:

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Given the following function:

. . . . .\(\displaystyle V(t,\, d_u,\, V_u)\, =\, \begin{cases}V_u\, \ln(t\, -\, d_u\, t\, l)&\mbox{for }\, t\, \geq\, d_u \\ \theta &\mbox{for }\,t\, <\, d_u\end{cases}\)

...maximize the following:

. . . . .\(\displaystyle \dfrac{V(t)}{t}\)

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Please reply with corrections or confirmation.

When you reply, please explain the relationship between the function V(t, d_u, V_u), V_u, and V(t). Also, what is the meaning of the "ell" after the "tee" in the natural log? Also, which, if any, of the variables are constants, or are related (how?) to each other? How does "theta" relate to anything? What other information are you given about this exercise?

Please also include a clear listing of your thoughts and efforts so far, as this will greatly help us in understanding what is going on and where you're getting stuck. Thank you!