2. Suppose you find that a firm produces and sells x blenders annually, with their total profit (in hundreds of dollars) given by

p(x)=1.11x-23.943-0.003x^2

a) Using a graphing utility produce the graph of P in such a way that the appropriate features of the graph are displayed. Print this graph and include it with your submission.

In 1-3 sentences explain how you chose what features of the graph you are attempting to display and why?

b) Does the graph of P ever dip below the x-axis? In 1-3 sentences explain what this could indicates using the vocabulary from part 1.

c) Using the graph obtained in part a) estimate the following in interval notation:

i. For what values of x will P be negative?

ii. For what values of x will P be positive?

d) Determine when P (x) = 0 and in 1-3 sentences explain what it indicates using the vocabulary from part 1.

e) Using algebraic methods determine how many blenders must the company produce and sell in order to maximize profit?

f) For what values of x is the profit increasing?

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