A closed rectangular box has to be constructed as follows:
- Dimensions: length (f), width (w) and height (h).
- The length (l) of the base has to be 3 times its width (w).
- The volume has to be 5 m3.
The material for the top and the bottom parts costs R15 per square metre and the material for the sides costs R6 per square metre.
9.1 Show that the cost to construct the box can be calculated by: Cost = 90w2 + 48wh (4)
9.2 Determine the width of the box such that the cost to build the box is a minimum. (6)
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