3. Let E denote the region in the plane enclosed by the line r = 60, the line y = -0.04r + 5, and the parabola y = 0.00062 -0.08r + 3. (a) Make a detailed sketch of the region E (you may use plotting software to help). (b) Write down an integral representing the area of E. Explain how you arrived at your integral. (c) Compute the integral you gave in (b). (d) Suppose that, in the manufacture and sale of some product (perhaps indestructible Buc-ce mugs), the marginal revenue and marginal cost at a production level of r units are given by R'(x) = -0.04x +5 and ("(x) = 0.0006r2 -0.08x +3, respectively (measured in thousands of dollars per unit). Thus the graphs of R' and (", together with the line x = 60, represent the boundary curves of the region E. In this context, what does the integral you computed in (c) represent? Explain your