Chapter 6.4, Problem 31MCQ

To determine

If the cost of producing $\left(x\right)$ cell phones in a factory is $C\left(p\right)=5p+60$ and cell phones produced in $\left(h\right)$ hours is $P\left(h\right)=40h$ then find the composition function.

Answer to Problem 31MCQ

The composition function is $\left(C\circ P\right)\left(h\right)=200h+60$ .

Explanation of Solution

Given information: The given functions are $C\left(p\right)=5p+60$ and $P\left(h\right)=40h$ .

Calculation: The composition function $\left(C\circ P\right)\left(h\right)$ is evaluated as,

  $\begin{array}{c}\left(C\circ P\right)\left(h\right)=C\left[P\left(h\right)\right]\\ =C\left[40h\right]\\ =5\left(40h\right)+60\\ =200h+60\mathrm{....}\left(1\right)\end{array}$

Hence the composition function is $\left(C\circ P\right)\left(h\right)=200h+60$ .

To determine

Find the cost of producing cell phones for 8 hours.

Answer to Problem 31MCQ

The cost of producing cell phones for 8 hours is $1660$ .

Explanation of Solution

Given information: The given functions are $C\left(p\right)=5p+60$ and $P\left(h\right)=40h$ .

Calculation: From (1), $\left(C\circ P\right)\left(h\right)=200h+60$ . Therefore substitute $h=8$ in (1),

  $\begin{array}{c}\left(C\circ P\right)\left(8\right)=200\left(8\right)+60\mathrm{....}\left(\text{For }h=8\right)\\ =1660\end{array}$

Hence the cost of producing cell phones for 8 hours is $1660$ .