Analyzing a Manager's Profit Calculation
A company's daily profit (P, in thousands of dollars) is a function of the number of units (x) it produces, given by P = 50 * ln(x). The number of units produced is determined by the number of hours the factory operates (h), where x = 20h. A manager analyzes the relationship and states: 'The rate at which profit changes with respect to production is dP/dx = 50/x. To find how profit changes with respect to operating hours, dP/dh, I'll just substitute x=20h into my first result, which gives 50/(20h) or 2.5/h.' Is the manager's final expression for dP/dh correct? Explain your reasoning by describing all the mathematical components required for the correct calculation.
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