A factory’s weekly production costs y and its weekly production quantity x are related by the equation y² - 5x³ = 4, where y is in thousands of dollars and x is in thousands of units of output.

(a) Use implicit differentiation to find a formula for dy/dx, the marginal cost of production.

(b) Find the marginal cost of production when x = 4 and y = 18.

(c) Suppose that the factory begins to vary its weekly production level. Assuming that x and y are differentiable functions of time t, use the method of related rates to find a formula for dy/dt, the time rate of change of production costs.

(d) Compute dy/dt when x = 4, y = 18, and the production level is rising at the rate of .3 thousand units per week (that is, when dx/dt = .3 ).