The profit made when $t$ units are sold, $t 0$, is given by $P = t ^ { 2 } - 27 t + 176$. Determine the number of units to be sold in order for $\mathrm { P }

Question

The profit made when $t$ units are sold, $t > 0$, is given by $P = t ^ { 2 } - 27 t + 176$. Determine the number of units to be sold in order for $\mathrm { P } < 0$ (a loss is taken).

Quizplus · Accepted Answer

To find the range of $t$ for which $P < 0$, we need to solve the inequality $t^2 - 27t + 176 < 0$. Factoring the quadratic expression, we get $(t - 11)(t - 16) < 0$. This inequality holds true when $t$ is between the roots, 11 and 16, hence $11 < t < 16$.

The Profit Made When ttt Units Are Sold t>0t > 0t>0 , Is Given By

The Profit Made When $t$ Units Are Sold $t > 0$ , Is Given By