I am working on a business calculus problems that is regarding maximum/minimum profit. I have the answer that my teacher provided; however, I am unsure of any of the work. Can you please help me understand the steps. Thank you.

I have attached both the question and the problem in an image.

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Question 1 A company manufactures and sells 1 tablets per month. The monthly price demand equation and cost function are given; respectively, as follows: Pce-Demand: p = sun H.025): fat ti r: x 5 20.009 Cust: C(IJ = 35D: + S {A} How mam.t tablets should the company manufacture to maximize profit? {Bl 1What is the maximum I'I'ion'thwI prot? {Ci How much should the company charge for each tablet to realite the maximum monthly prot? Answer: Max prot is $115,000 when 34.000 tablets are manufactured and sold for $425 each