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4. The demand for the monopolist's product in terms of the number of units x() she or he sell depends on both the price P(t) of the good and the rate of change in price P'(t) : Let the demand function and cost function be x(1) = aP() + bP'(t) + c. and z(x) = mx" + nx + k Assuming P(0) = P, and the desired price at time Tis P(7) . Find the I pricing policy to maximize profit Max [P()x() - z(x)|dt over 0ST. Also check the second order condition