A rectangular container with open top is required to

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7) A rectangular container with open top is required to have a volume of 16 cubic meters. Also, one side of the rectangular base is required to be 4 meters long. If material for the base costs $8 per square meter, and material for the sides costs $2 per square meter, find the dimensions of the container so that the cost of material to make it will be a minimum.
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8) A rectangular box with open top is to be constructed from a rectangular piece of cardboard 80 cm by 30 cm, by cutting out equal squares from each corner of the sheet of cardboard and folding up the resulting flaps. Find the dimensions of the box of maximum volume made by these conditions.
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