edfinity My Courses Q search Section 3.4 (1 point) A rectangular storage contain

Question

edfinity My Courses Q search Section 3.4 (1 point) A rectangular storage container with an open top is to have a volume of 20 cubic meters. The length of its base is twice the Material for the base costs 11 dollars per square meter. Material for the sides costs 7 dollars per square meter. Find the cost of width. materials for the cheapest such container. Total cost example, if your answer is 1.005, enter S1.10 including the dollar sign and second decimal place.) (Round to the nearest penny and include monetary units. For Submit

Explanation / Answer

Solution:

V = L * b * h

=> 20 = 2 b * b * h

=> h = 10 / b^2 ......(1)

now cost , C = 11 * L*b + 14 * b * h + 14 * L * h

=> C = 22 b ^2 + 140 / b + 280 / b

=> C = 22b^2 + 420 / b

=> C' = 44 b - 420/b^2

putting C' = 0

=> b^3 = 420/44

=> b = 2.12

Hence cost = 22 * (2.12)^2 + 420/2.12

=> C = 297 dollors

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