A rm can produce a quantity q of its product at a cost given by 0(9) = (13 - 3q2 + 3g- The market price of its product is p per unit where p is a constant and, for any given value of p} the rm will always produce an amount q that will maximise its prot. (a) Write down the rm's prot function, 7r(q). Find and classify the stationary points of 7r(q). (b) For each value of p} nd the maximum value of 7T(q) and the value(s) of q at which it occurs. (c) Write down an expression for the rm's supply function. Does the rm have an inverse supply function? Justify your answer by nding an inverse supply function or explaining Why no such function exists