I may be way off here, but...
we have profit = revenue minus cost, i.e.
s = r - k
and revenue = quantity sold times price, ie.
r = 1,000,000 xp
and IF (but here's where I wouldn't like to bet) we can say that the cost to produce x million units increases over time according to the function
k(x,t) = 200 xt
... then (and only if a picture helps, pardon if not) we have
... is the product rule. Straight lines differentiate downwards with respect to t.
Also, we can use...
... the chain rule, to express as the product of and i.e...
Straight continuous lines still differentiate downwards with respect to t, and the straight dashed line similarly but with respect to the dashed balloon expression (which is the inner function of the composite and hence subject to the chain rule).
And we can find by implicitly differentiating the demand formula...
Solving the bottom row gives...
Maybe solving the bottom row there will help with a and some of b (though quite possibly in the wrong order).
Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
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