Question

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

cost= 4LW+2*2LH+2*2WH

now, cutting out the box,
L=12-2h
W=10-2h
substiture those for L and W in the cost equation, then take the derivative of cost/dh and set to zero, solve for h, then L, then W.

Answer 2

h=11/6
L=25/3
W=19/3