A business analyses their profit margins, and finds that if they produce and sell x items annually, the total profit (in dollars) can be represented by: P(x)=-8x+0.3x^(2)-0.0013x^(3)-172

Question

How many items must the business produce to break even?

What is the largest possible profit the business could have? (round to the nearest cent)

Answer 1

The easiest method is to plot P(x).

a) The zero crossings or break even points are ≈ 49 or 196. Choose 49

b) The max profit is when x = 139, P(139)≈$1021.00