Solve the rational inequality. Write the solution set in interval notation.
-The cost of producing t units i $C = 2 t ^ { 2 } + 7 t$ t, and the revenue generated from sales is $\mathrm { R } = 3 \mathrm { t } ^ { 2 } + \mathrm { t }$ Determine the number of units to be sold in order to generate a profit.
A) t 0
B) t 6
C) t 8
D) t 7

Question

Solve the rational inequality. Write the solution set in interval notation.
-The cost of producing t units i $C = 2 t ^ { 2 } + 7 t$ t, and the revenue generated from sales is $\mathrm { R } = 3 \mathrm { t } ^ { 2 } + \mathrm { t }$ Determine the number of units to be sold in order to generate a profit.
A) t > 0
B) t > 6
C) t > 8
D) t > 7

Quizplus · Accepted Answer

The profit is given by $P = R - C = 3 t ^ { 2 } + t - 2 t ^ { 2 } - 7 t = t ^ { 2 } - 6 t$. To generate a profit, we need $P > 0$, which is equivalent to $t ^ { 2 } - 6 t > 0$. Factoring, we get $t(t - 6) > 0$. The solution set is $t < 0$ or $t > 6$. Since we are interested in the number of units to be sold, we discard the negative solution. Therefore, the answer is $t > 6$.

Solve the Rational Inequality C=2t2+7tC = 2 t ^ { 2 } + 7 tC=2t2+7t

Solve the Rational Inequality $C = 2 t ^ { 2 } + 7 t$