The cost C of producing t units is given by $C ( t ) = 3 t ^ { 2 } + 7 t$ and the revenue R generated from selling t units is given by $R ( t ) = 4 t ^ { 2 } + t$. For what values of t will there be a profit?
A) $t 8$
B) $t 6$
C)$t 0$
D) $t 7$

Question

The cost  C  of producing  t  units is given by $C ( t ) = 3 t ^ { 2 } + 7 t$ and the revenue  R  generated from selling  t  units is given by $R ( t ) = 4 t ^ { 2 } + t$. For what values of  t  will there be a profit?
A) $t > 8$
B) $t > 6$
C)$t > 0$
D) $t > 7$

Quizplus · Accepted Answer

Profit occurs when revenue exceeds cost, so we set $R(t) > C(t)$ and solve for $t$. This gives $4t^2 + t > 3t^2 + 7t$, simplifying to $t^2 - 6t > 0$, which factors to $t(t - 6) > 0$. This inequality is satisfied for $t > 6$.

The Cost C of Producing T C(t)=3t2+7tC ( t ) = 3 t ^ { 2 } + 7 tC(t)=3t2+7t

The Cost C of Producing T $C ( t ) = 3 t ^ { 2 } + 7 t$