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.

Question

Advanced Placement (AP)

Lorenzo Bowman

26 July, 22:22

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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Spookey · Answer 1

Using the given values, we have the equation

P (x) = 1000 + ∫ MC (s) ds from 0 to 5t

evaluating the integral

P (x) = 1000 + M (5t) C (5t) - M (0) C (0)

where the value of the functions

M and C should be defined to solve the equation explicitly in terms of t