Question

A rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Material for the base costs $15 per square meter. Material for the sides costs $9 per square meter. Find the cost of materials for the cheapest such container. (Round your answer to the nearest cent.)

Answer 1

L = 2 W
B = L x W = 2 W²
Side Area = 2 W H + 2 L H = 2 H ( W + L ) = 6 H W
V = 2 W² H = 10
H = 5 / W²
Cost = 15 * 2 W² + 9 * 5/W
= 30 W² + 270/ W 
C ` = 60 W - 270 / W² 
= ( 60 W² - 270 ) / W² = 0
60 W² = 270
W ² = 270 : 60
W² = 4.5
W = √ 4.5 = 2.12
Cost (min) = 15 * 2 * 4.5 + 30 / 2.12 = 135 + 14.15 = $149.15
Answer: The cost of materials for the cheapest such container is $149.15.