2 Laura owns and operates Aunt Lindas Pecan Pies She has lea

2. Laura owns and operates Aunt Linda\'s Pecan Pies. She has learned that her profits, Pix), from the sale of x cases of pies, are given by P(x) 150x-x a. The company will break-even\" when the profit is zero. How many cases of pies should Laura sell in order to break-even? (Solve for x when P(x)-0) b. How many cases of pies should she sell in order to maximize profit? c. What is the maximum profit? 3. For the function f(x) = 3x4-4x3 + x2 + 6x-2 a. State the degree of the polynomial. b. State the number of zeros the polynomial function will have. c. Use the Rational Zero Theorem to list all of the possible rational zeros d. Use your calculator to determine which numbers in the list of rational zeros are probable rational zeros

Solution

2 a) P(x) = 150x -x^2

P(x) =0 ; 150x -x^2 =0

x(150 -x) =0

x =0 and x= 150 pies

b) To maximise profit: dfind derivative of P(x) and equate it to 0

P\'(x) = 150 -2x =0

x = 75 pies give max. profit

c) maximium profit : plu x= 75 in P(x)

P(75) = 150*75 -75^2 = $5625

3. P(x) = 3x^4 -4x^3 +x^2 +6x -2

a) degree = highest tem = 4

b) No. of zeros = 04