2020 Nov P1 Q9

Question 9

A closed rectangular box has to be constructed as follows: Dimensions: length $(l)$ , width $(w)$ and height $(h)$ . The length $(l)$ of the base has to be $3$ times its width $(w)$ . The volume has to be $5\,m^3$ . 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: $Cost=90w^2+48wh$	$(4)$
$9.2$	Determine the width of the box such that the cost to build the box is a minimum.	$(6)$
		$\textbf{[10]}$