The profit from the supply of a certain commodity is modeled as P(q) = 77qe^{-0.2q} dollars where q is the number of units produced. 0 ? q ? 100 (a) Write an expression for the rate of change of profit. (Be sure to use q as the independent variable.) P'(q) = -14.6qe^{-0.2q} + 73e^{-0.2q} dollars per unit (b) At what production level in the domain 0 ? q ? 100 is the rate of change of profit zero? (Round your answer to the nearest whole number.) q = 5 units (c) What is profit at the production level found in part (b)? (Round your answer to two decimal places.) $ 134.29
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First, we are given the profit function as: P(q) = 77qe (a) We need to find the rate of change of profit with respect to the number of units produced, which is the derivative of the profit function with respect to q: Show more…
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