The profit made when $t$ units are sold, $t 0$, is given by $P = t ^ { 2 } - 30 t + 200$. Determine the number of units to be sold in order for $\mathrm { P } 0$ (a profit is made).

Question

The profit made when $t$ units are sold, $t > 0$, is given by $P = t ^ { 2 } - 30 t + 200$. 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 for which $P > 0$, we solve the inequality $t^2 - 30t + 200 > 0$. Factoring the quadratic equation gives $(t-20)(t-10) > 0$, which means the profit is positive when $t > 20$ or $t < 10$.

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