You have been asked to design a rectangular box with a square base and an open top. The volume of the box must be 1715cm3. Determine the dimensions of the bin that will minimize the surface area, where x is the length of each side of the base and y is the height of the box.

x=15.08 cm

y=7.54 cm

Step-by-step explanation:

We are given that

Volume of box=1715 cubic cm

Side length of base=x

l=b=x

Height of box=h=y

Volume of box=lbh=x^2y

Surface area of box=Area of bottom+area of four faces=

Differentiate w.r.t x

Again differentiate w.r.t x

Substitute x=15.08

Hence, the surface area is minimum at x=15.08 cm

(x, y)→(x − 8, y − 7)

step-by-step explanation:

enjoy!

it would open into a square depending on the type of envelope i’m not sure about the second part