Answer:
Step-by-step explanation:
Given
Volume of box is 800 cm^3
[tex]V=800 cm^3[/tex]
Let the dimension of base is [tex]L\times L[/tex] and height of box be h
[tex]V=L^2\times h[/tex]
cost base [tex]c_1=L^2\times 5=5L^2[/tex]
cost of sides [tex]c_2=(4Lh)\cdot 7[/tex]
[tex]c_2=28Lh[/tex]
Total Cost[tex]=c_1+c_2[/tex]
[tex]C=5L^2+28Lh [/tex]
[tex]C=5L^2+28L\cdot \frac{800}{L^2}[/tex]
[tex]C=5L^2+\frac{800\times 28}{L}[/tex]
differentiate C w.r.t L to get maximum/minimum Value
[tex]\frac{\mathrm{d} C}{\mathrm{d} L}=10L-\frac{800\times 28}{L^2}[/tex]
[tex]L=13.05 cm[/tex]
[tex]h=4.69 cm[/tex]
