MAT 171 Lab 3 Summer Name:________________________________________________________ Date:_____________________________________ Solve each of the following problems. Show all your work for credit! 1. Concert Tickets. (section 3.1) The revenue at the Assembly Center depends on the number of seats sold for the Willie Williams and the Wranglers concert. At $10 per ticket, they will fill all 8000 seats. The manager knows that for every $1 increase in the price, 500 tickets will go unsold. If the revenue in dollars, R(p), is given by R( p) 500 p 13,000 p , where p is the price per ticket sold. 2 (a) What ticket price will produce a maximum revenue? What is the maximum revenue? You must show this algebraically. (b) Find the number of unsold seats that resulted in this maximum revenue given the following n 13000 500 p where n is the number of seats sold and p is the price. You must show this algebraically. Page 1 of 2 MAT 171 Lab 3 Summer Name:________________________________________________________ Date:_____________________________________ 2. Solving a polynomial equation (section 3.2 and 3.3) f ( x) 6 x3 25x 2 24 x 5 (a) Using the above function, demonstrate use of the Rational Root Test to list (unrepeated) all the potential rational zeros. (b) Using the above function, demonstrate the following: (i) selecting divisors from the potential rational zeros, (ii) using Remainder Theorem to check whether it is a zero, (iii) whenever it is a zero use synthetic division to find the depressed polynomial, and (iv) repeating until you have the function down to a \"solvable\" function. (c) Once you have the function down to a \"solvable function\