APPLIED MATHEMATICS Assignment # 3 GROUP 6 : Charlotte O. Tang Ritchie Roi Chua Ramon Naguiat Mark Anthony Salazar Mary Jane Pagmulotan Tong Ya

A manufacturer can produce radios at a cost of Php48.00, and estimates that, if they are sold for P pesos each, consumers will buy 50-p radios a day. At what unit price should the manufacturer sell the radios to maximize his profit? What is the maximum profit he can obtain? THE PROBLEM : Page 257, # 25

Let x be the number of radios y be the profit y be the profit *At P pesos each, x=50-p y = (x) (p) - 48x y = (50-p)(p) - 48(50-p) = 50p-p p y = -p 2 +98p-2400 D(y) = -2p+98 ; Setting D(y) = 0 : - 2p + 98 = 0 p = 49 When p = 49 : y = - (49) (49) = y = 1

To check whether p = 49 is a Min/Max : D 2 (y) = - 2 Since D 2 (y) < 0 : p = 49 is a MAXIMUM pt. p = 49 is a MAXIMUM pt. At Php per radio, the manufacturer maximizes his profit, the maximum profit that will be obtained is Php 1.00