A 10 cm x 12 cm rectangular sheet that is used to make a box with open top is to be lined with cushion. if the cushion material for the sides costs four times per square centimeter as that of material for the bottom, find the dimensions of the box if the cost is to be minimized.

Answer 1

I assume this is the usual corner-cut problem. So, if the cuts have length x, then the cost of the material is

c = (12-2x)(10-2x) + 4(2x(10-2x)+2x(12-2x))

Hmm. I guess x" corners are not cut and the rest folded up.