The weekly cost C of producing x units in a manufacturing process is given by
[tex]C(x)=60x+750[/tex]
The number of units x produced in t hours is given by
[tex]x(t)=50t[/tex]
(a) The composite function C(x(t)) is given by
[tex]\begin{gathered} C(x)=60x+750 \\ C(x(t))=60(50t)+750 \\ C(x(t))=3000t+750 \end{gathered}[/tex]
The function C(x(t)) gives us the cost of production for t hours.
(b) The number of units produced in 4 hours is given by
[tex]\begin{gathered} x(t)=50t \\ x(t)=50(4) \\ x(t)=200 \end{gathered}[/tex]
200 units will be produced in 4 hours.
(c) Let us graph the function C(x(t)) = 3000t + 750 to find the value of t for which the cost increases to $15,000
As you can see, the value of t is 4.75 hours when the cost is $15,000.
Therefore, 4.75 hours must elapse until the cost increases to $15,000.
