Question: Tim runs a textile company that manufactures T-shirts. The profit made by the company is modeled by the function p = s2 + 9s - 1620, where s is the number of T-shirts sold. Find the least number of T-shirts to be sold so that Tim does not end up in a loss.
A ) 40 B ) 36 C ) 42 D ) 38
Steps to derive
1p = s2 + 9s - 1620 [Original equation.]
2 0 = s2 + 9s - 1620 [Replace p with 0.]
3s = {-(9)±[9²-4(1)(-1620)]}2(1) [Substitute the values in the quadratic formula: a = 1, b = 9 and c = -1620.]
4 = -9±(81+6480)2 [Simplify.]
5 = -9±65612 [Simplify inside the radical.]
6 = -9±812 [Simplify the radical.]
7s = 722 = 36 [Consider only the positive value of s. s can't be negative as it represents the number of T-shirts.]
