RD Enterprises is designing an open top box to transport 400 yd³ of material from one place to another in several trips. Two of the sides and bottom of the box can be made of a free material that the company has on hand, but only 8 yd² of the material is available. Because of the hauling regulations associated with transporting this material, the two ends of the box must be made from a heavyweight material that costs $1000 per yd². Each trip costs $10.

(a) Let x, y, and z represent the length, width, and height (in yards) of the box, respectively. If we want to use all of the free material, show that the total cost in dollars is given by the function

subject to the constraint 2xz + xy = 8.

(b) Use the Solver feature on a spreadsheet to find the dimensions of the box that minimize the transportation cost, subject to the constraint.

Transcribed Image Text:

f(x, y, z) = 4000 xyz + 2000yz