Book Maths Puzzle Algebra

Is there a software to write a linear system of equations (it's actually an optimization problem), and solve it. it's of this kind
minF= Y.Y + w(X.X)+ s(Z.Z) with
Y= a + bI + cD + dI* + eD*
X= f + gI + hD + iI* + jD*
Z= k + lI + mD + nI* + oD*

All lower case are parameters, and adctually they have indices (is there something to write that easily, it's a pain under Word...)
I need to diiferentiate F with respects to I and D, then write I and D as functions of I* and D*. I can do it myself but it takes a really long time and even longer to type it, is there a solver for that??
thanks so much for your help

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Book Other Question

A rectangular piece of sheet metal with an area of 1200 in^2 is to be bent into a cylindrical length (right circular cylinder) of stovepipe having a volume of 600 in^3. What are the dimensions of the sheet metal? Sketch the graph of each function. state the domain and range, and whether the function is increasing or decreasing. identify any aysmptotes.
f(x)=2^x-3