The monthly cost C of running the machinery in a factory for t hours is given by $C ( t ) = 40 t + 400$ The number of hours t needed to produce x products is given by $t ( x ) = 6 x$ . Find the equation representing the cost C of manufacturing x products.
A) $C ( x ) = 46 x + 440$
B) $C ( x ) = 240 x + 16,000$
C) $C ( x ) = 40 x + 406$
D) $C ( x ) = 46 x + 400$
E) $C ( x ) = 240 x + 400$

Question

The monthly cost C of running the machinery in a factory for t hours is given by​ $C ( t ) = 40 t + 400$ The number of hours t needed to produce x products is given by $t ( x ) = 6 x$ . Find the equation representing the cost C of manufacturing x products.
A) $C ( x ) = 46 x + 440$
B) $C ( x ) = 240 x + 16,000$
C) $C ( x ) = 40 x + 406$
D) $C ( x ) = 46 x + 400$
E) $C ( x ) = 240 x + 400$ ​

Quizplus · Accepted Answer

To find the cost $C(x)$ of manufacturing $x$ products, substitute $t(x) = 6x$ into $C(t) = 40t + 400$, resulting in $C(x) = 40(6x) + 400 = 240x + 400$.

The Monthly Cost C of Running the Machinery in a Factory