The cost of producing x units of a certain commodity is given by P (x) = 1000 + ∫ ^x to 0 MC (s) ds, where P is in dollars and M (x) is marginal cost in dollars per unit. B. Suppose the production schedule is such that the company produces five units each day. That is, the number of units produced is x = 5t, where t is in days, and t = 0 corresponds to the beginning of production. Write an equation for the cost of production P as a function of time t. C. Use your equation for P (t) from part B to find dP/dt. Be sure to indicate units and describe what dP/dt represents.
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