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. Mater
ial 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.)
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.
