Question A rectangular box is constructed in such a way that the length (I) of the base

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A rectangular box is constructed in such a way that the length (I) of the base is three times as long as its width. The material used to construct the top and the bottom of the box costs R100 per square metre. The material used to construct the sides of the box costs R50 per square metre. The box must have a volume of 9 m³. Let the width of the box be x metres. 11.1 11.2 11.3 1 Determine an expression for the height (h) of the box in terms of x. 1200 Show that the cost to construct the box can be expressed as C =- X -+600x². Calculate the width of the box (that is the value of x) if the cost is to be a minimum. A rectangular box is constructed in such a way that the length (I) of the base is three times as long as its width. The material used to construct the top and the bottom of the box costs R100 per square metre. The material used to construct the sides of the box costs R50 per square metre. The box must have a volume of 9 m³. Let the width of the box be x metres. 11.1 11.2 11.3 1 Determine an expression for the height (h) of the box in terms of x. 1200 Show that the cost to construct the box can be expressed as C =- X -+600x². Calculate the width of the box (that is the value of x) if the cost is to be a minimum.