pre - calculus ic sem a jones\ncomposition of functions and modeling\na manufacturer of widgets finds that…

pre - calculus ic sem a jones\ncomposition of functions and modeling\na manufacturer of widgets finds that the production cost, c, in dollars per unit is a function of the number of widgets produced. the selling price, s, of each widget in dollars is a function of the production cost per unit.\nc(x)=-0.1x² + 100\ns(c)=1.4c\nwhat is the selling price per widget as a function of the number of widgets produced, and what should the selling price be if 15 widgets are produced?\ns(c(x))=-0.14x² + 140; $144.41\nc(s(x))=-0.196x² + 100; $55.90\ns(c(x))=-0.14x² + 140; $108.50\nc(s(x))=-0.196x² + 100; $108.64

pre - calculus ic sem a jones\ncomposition of functions and modeling\na manufacturer of widgets finds that the production cost, c, in dollars per unit is a function of the number of widgets produced. the selling price, s, of each widget in dollars is a function of the production cost per unit.\nc(x)=-0.1x² + 100\ns(c)=1.4c\nwhat is the selling price per widget as a function of the number of widgets produced, and what should the selling price be if 15 widgets are produced?\ns(c(x))=-0.14x² + 140; $144.41\nc(s(x))=-0.196x² + 100; $55.90\ns(c(x))=-0.14x² + 140; $108.50\nc(s(x))=-0.196x² + 100; $108.64

Answer

Explanation:

Step1: Find the composition $S(C(x))$

Given $C(x)= - 0.1x^{2}+100$ and $S(C)=1.4C$. Substitute $C(x)$ into $S(C)$: $S(C(x))=1.4(-0.1x^{2}+100)=-0.14x^{2}+140$.

Step2: Calculate the selling - price when $x = 15$

Substitute $x = 15$ into $S(C(x))$: $S(C(15))=-0.14\times15^{2}+140=-0.14\times225 + 140=-31.5+140 = 108.5$.

Answer:

$S(C(x))=-0.14x^{2}+140;$108.50$