(4) Consider a product whose unit cost is $3/item and whose demand function is given by 50000 D(p) = 1+p? (a) What is the formula for the profit function associated with this product? (This is like problem 3 from midterm 2) (b) Use Calculus to find the optimal price p for our product so that the profit is maximized. What is the profit in this case?

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A: Solving

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A: limx→a f(x)=L if and only if limx→a- f(x) =L=limx→a+ f(x) .

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A: Differentiate f(x)

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A: This question is related to derivative, we will solve it using given information.

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A: We will Break this question into two parts.

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A: Here we have to find the intervals where the function is increasing and decreasing.

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A: We will find the area and cost.

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A: We can solve this as follows:

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