For starters, if ~E \le B~, then the engineers are at least as fast as the Cow-Bot at installing modules, so they might as well just install all of them themselves. This will take them ~N \times E~ minutes.

Otherwise, the Cow-Bot is faster, so our goal is to have it install as many modules as possible, with the only limitation being the modules' ~M~ requirements. As such, let's start by sorting the modules in non-decreasing order of their ~M~ values, which can be done in ~\mathcal O(N \log N)~ time. The modules at the end (with the largest ~M~ values) are the least likely to be able to be installed by the Cow-Bot before it's too late, so the engineers should prioritize installing those. On the other hand, the modules at the start (with the smallest ~M~ values) will be the ones which the Cow-Bot should go ahead and install whenever it can.

These ideas suggest the following greedy solution, in which we'll simulate the modules' installation. Let ~m~ be the number of modules installed so far (which we'll iterate upwards from ~0~ to ~N-1~), ~i~ be the first module which hasn't yet been installed (initially module ~1~ in the sorted list), and let ~t~ be the total amount of time taken so far (initially ~0~). At each step, if ~m \ge M_i~, then the Cow-Bot is currently able to install the ~i~-th module, so it should certainly do so – in this case, we'll increment ~i~ by ~1~, and ~t~ by ~B~. Otherwise, there's no module currently available for the Cow-Bot to install, so the engineers must go ahead and install one from the end – in this case, we'll just increment ~t~ by ~E~. This simulation process takes ~\mathcal O(N)~ time.