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Rubbermaid Easy Find Lid 24-Piece Food Storage Container Set List Price: $19.99 Sale Price: $10.47 Average Rating:   |
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These containers have clear sides - no guessing at what might be inside. They also feature lids that are airtight, yet easy to open thanks to the notch in the base that lines up with the protruding part of the lid, allowing your finger to get some leverage without ruining your manicure... |
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A rectangular storage container with an open top is to have a volume of 20 cubic meters. The length of its bas?
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 width. Material for the base costs 20 dollars per square meter. Material for the sides costs 3 dollars per square meter. Find the cost of materials for the cheapest such container.
Minimum cost = ________________
Let, the length of the base be 2x, width x and height y.
Cost, C = 20(2x²) + 3(4xy + 2xy) = 40x² + 18xy ................. (1)
Also, y = 20/2x² = 10/x² ........................................ (2)
From (1) and (2) we have,
C = 40x² + 180/x ;
dC/dx = 80x - 180/x² ;
The cost will have a minimum if dC/dx = 0.
Therefore,
80x - 180/x² = 0 ;
80x = 180/x² ;
x³ = 180/80 = 2.25 ;
x = 1.3104 metres.
y = 10/x² = 10/1.7171 = 5.8238 metres.
Minimum cost = 40x² + 18xy = 40 X (1.3104)² + 18 X (1.3104 X 5.8238) dollars.
= 206.0533 dollars.