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If the relationship between the number x of watches that can be sold and the price p (in dollars) per watch is given by 5x + p = 320; what price should be charged, and how many watches should be manufactured per week in order to maximize the profit?
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We have \(p=320-5x\). We want to maximize the prophet which, that's maximizing the prize times the number of sold watches. So, let's \(f(x)=x p(x)=320x-5x^2\). f is maximum at \(320-10x=0 \implies x=32\) watches. The prize for maximum prophet is then \(p=320-5(32)=$160\).
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