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A car manufacturer company faces a demand schedule: p = -5q 2 + 180 And a total cost schedule: TC = -4q 3 - 183q

A car manufacturer company faces a demand schedule: p = -5q2 + 180

And a total cost schedule: TC = -4q3 - 183q + 214

Please find the following:

a- What output level (if any) will maximize the profits?

b- What output level (if any) will minimize the profits?

c- What is the logic behind using the differential calculus of different orders to solve this problem? Considering this problem, what does each of the 1st and 2nd order differential lead you for?

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