A box of volume 180 m3 with square bottom and no top is constructed out of two different materials. The cost of the bottom is $40/m2 and the cost of the sides is $30/m2 . Find the dimensions of the box that minimize total cost. (Let s denote the length of the side of the square bottom of the box and h denote the height of the box.)

Side of square bottom=6.46 m

Height of box=4.31 m

Step-by-step explanation:

Let s be the side bottom

Height of box=h

Volume of box=

Volume of box=

Cost of bottom=$40 per square  m

Cost of sides =$30 per square  m

Total cost=

Differentiate w.r.t s

Again,differentiate w.r.t s

Substitute s=6.46

Hence, the cost is minimum at s=6.46

Side of square bottom=6.46 m

Height of box=4.31 m

step-by-step explanation:

see if this :

$450 is the answer.

step-by-step explanation:

30% of 450 = 135

450-135=315