The profit made when t units are sold, $t 0$ is given by $P = t ^ { 2 } - 29 t + 204$ Determine the number of units to be sold in order for $\mathrm { P } 0$ C) $12 \text { units }

Question

The profit made when t units are sold, $t > 0$ is given by $P = t ^ { 2 } - 29 t + 204$ Determine the number of units to be sold in order for $\mathrm { P } < 0$ (a loss is taken). A) $t < 12 \text { units or } t > 17 \text { units }$ B) $t > 0$ C) $12 \text { units } < t < 17 \text { units }$ D) t=12 units or t=17 units

Quizplus · Accepted Answer

To determine when $P < 0$, we factor the quadratic equation $P = t^2 - 29t + 204$. Factoring gives $(t - 12)(t - 17) = 0$, so the roots are $t = 12$ and $t = 17$. For $P$ to be negative, $t$ must be between these two roots, hence $12 < t < 17$.

The Profit Made When T Units Are Sold t>0t > 0t>0

The Profit Made When T Units Are Sold $t > 0$