Question "A company offers the following schedule of charges: $30 per thousand for orders of 50,000 or less, with the charge decreased by 37.5 cents for each thousand above 50,000. Find the order size that makes th company's receipts a maximum". Attempted Answer I understand that I have to formulate the above in some function, say f(x) where x is the number of orders, and then differentiate the function and equate the derivative to 0 to identify any maximum point. Yet, I am stuck as to putting the above into an equation. Some ideas that ran through my head included: 1) It's a linear equation where the gradient shifts after x= 50,000. 2) It requires two equations with different domains. Then I gave up. Help would be appreciated.
asked Feb 11, 2020 at 19:00
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$\begingroup$ Receipts obviously increase steadily for orders up to 50,000. So you can be sure your answer lies in the domain of orders higher than that. $\endgroup$
Commented Feb 11, 2020 at 19:11