Solve the problem.
-The profit made when $\mathrm { t }$ units are sold, $\mathrm { t } > 0$ , is given by $\mathrm { P } = \mathrm { t } ^ { 2 } - 28 \mathrm { t } + 187$ . Determine the number of units to be sold in order for $\mathrm { P } > 0$ (a profit is made) .

Question

Solve the problem.
-The profit made when

\mathrm { t }

units are sold,

\mathrm { t } > 0

, is given by

\mathrm { P } = \mathrm { t } ^ { 2 } - 28 \mathrm { t } + 187

. Determine the number of units to be sold in order for

\mathrm { P } > 0

(a profit is made) .

Quizplus · Accepted Answer

To determine the number of units $t$ for which $P > 0$, we solve the inequality $t^2 - 28t + 187 > 0$. Factoring or using the quadratic formula, we find the roots of the equation $t^2 - 28t + 187 = 0$ to be $t = 17$ and $t = 11$. Since $P(t)$ is a parabola opening upwards (coefficient of $t^2$ is positive), $P > 0$ outside the interval between the roots. Therefore, the profit is positive when $t > 17$ or $t < 11$.

Solve the Problem t\mathrm { t }t Units Are Sold t>0\mathrm { t } > 0t>0

Solve the Problem $\mathrm { t }$ Units Are Sold $\mathrm { t } > 0$