Answer:163.54$
Step-by-step explanation:
Given data
Volume of Storage(V)=[tex]{10m^3}[/tex]
Length=2breadth
Let Length be L,Breadth be & height be H
therefore
10=LBH
Now substitutes the values
10=2[tex]{B^2}H[/tex]
5=[tex]{B^2}H[/tex]
Now cost for base is [tex]{C_1}=2{B^2}\times10[/tex]
Cost for side walls is[tex]{C_2}={2LH}\times6+2BH}\times6[/tex]
Now total cost(C)=[tex]{C_1}+{C_2}[/tex]
C=20[tex]{B^2}H[/tex]+[tex]{2LH}\times6[/tex]+[tex]2BH}\times6[/tex]
C=20[tex]{B^2}H[/tex]+24BH+[tex]12BH[/tex]
C=[tex]20{B^2}+36B\times\frac{5}{B^{2}}[/tex]
Now Differentiating With respect to Breadth to get minimum cost
[tex]\frac{\mathrm{d} C}{\mathrm{d} B}=0[/tex]
[tex]we\ get\ B=\sqrt[3]{4.5}=1.65m[/tex]
[tex]L=3.30m[/tex]
[tex]H=1.836m[/tex]
and mimimum cost C
[tex]{C=163.54\$}[/tex]
