Minimizing surface Area United Parcel Service has contracted you to design an open box with a square base that has a volume of 5000 cubic inches. See the illustration.

(a) Express the surface area S of the box as a function of x.

(b) Using a graphing utility, graph the function found in part(a).

(c) What is the minimum amount of cardboard that can be used to construct the box?

(d) What are the dimensions of the box that minimize the surface area?

(e) Why might UPS be interested in designing a box that minimizes the surface area?

you mo despi is open bed with a squirt base that han s victim of JO0 cubk inches See the illustration fal Express the surface area 5 of the box as a function of I. (h) Using a graphing utility, graph the function found in part (a). (c) What is the minimum amount of cardboard that can be . moved to construct the box? (d) What are the dimensions of the box that minimize the surface area? d. (c) Why might UPS be interested in designing a box that minimizes the surface area