When a company produces and sells x thousand units per week its total weekly profit is P thousand dollars. where P = 100x/100 + x^2. The production level at t weeks from the present is x = 4 + 2t Find the marginal profit, dP/dx and the time rate of change of profit, dp/dt. How fast (with respect of time) are profits changing when t =8? dP/dx = (Type an expression using x as the variable.) dP/dt = (Type an expression using t as the variable.) The profits are at the rate of $ per week, when t equals 8. (Simplify your answer.)