Assume that the profit P made when t units are sold, $t 0$ is given by $P ( t ) = t ^ { 2 } - 28 t + 180$ For what values of t will there be a loss (that is, $\mathrm { P }

Question

Assume that the profit P made when t units are sold, $t > 0$ is given by $P ( t ) = t ^ { 2 } - 28 t + 180$ For what values of t will there be a loss (that is, $\mathrm { P } < 0 \}$ ? A) t=10 or t=18 B) $0 < \mathrm { t } < 10 \text { or } \mathrm { t } > 18$ C) $10 < t < 18$ D) $t > 0$

Quizplus · Accepted Answer

To determine when there is a loss, we need to find when $P(t) < 0$. Factoring the quadratic equation $P(t) = t^2 - 28t + 180$, we get $(t-10)(t-18) < 0$. This inequality is true for $t$ values between 10 and 18, hence $10 < t < 18$.

Assume That the Profit P Made When T t>0t > 0t>0

Assume That the Profit P Made When T $t > 0$