Answer:
[tex]f(x)=40x^2+\frac{100}{x}[/tex]
Step-by-step explanation:
Let [tex]x[/tex] denote side of the square base.
Area base=Area top:
[tex]Area=side\times side\\=x^2[/tex]
#Area of base and top is [tex]x^2[/tex] each
Given the volume as 5 cubic feet and side of base as x, height is:
[tex]Volume=x^2h\\5=x^2h\\h=5/x^2\\\\\therefore:\\Area \sides=4\times 5/x^2 \times x\\\\A_s=20/x[/tex]
Substitute the given prices to give the function for cost of material.
Top=30cents/ft, Base=10cents/ft and sides =50cents/ft:
[tex]f(x)=10x^2+30x^2+50(20/x)\\\\f(x)=10x^2+30x^2+\frac{100}{x}\\\\f(x)=40x^2+\frac{100}{x}[/tex]
The function for the cost of material is expressed as:[tex]f(x)=40x^2+\frac{100}{x}[/tex]
