The daily profit off a custom Tshirt shop can be modeled by

The daily profit off a custom T-shirt shop can be modeled by P(n) = n^2 + 60n-400, where and is the number of T-shirts produced each day and P(n) is The Profit made on that number. Rewrite this function in vertex form and determine the maximum daily profit.

Solution

P(n)=-n²+60n-400

P(n)=-(n²-60n)-400

P(n)=-(n²-60n+(-60_/2)²-(-60_/2)²)-400

P(n)=-(n²-60n+900-900)-400

P(n)=-(n²-60n+900)+900-400

P(n)=-(n-30)²+500

vertex is (30,500)

maximum daily profit =500