Given the demand function for a particular product is q(p)=(10-p^2)e^-p+3 for price p in thousands of...

Given the demand function for a particular product is q(p)=(10-p^2)e^-p+3 for price p in thousands of dollars. Suppose the cost of producing q units of this particular product is In(q).

a) Find the profit function in terms of p, pie(p). Use log properties to simplify the function.

b) Show there exists a solution p where pie(p)=0. (Cite any theorems used and do not solve for p)

c) Suppose we are current charging $3000 and we want to increase profit by 1%. Approximately how much percentage should we change the price of the product? (P is in thousands dollars)

Expert Solution

Rahul Sunny answered 3 months ago

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