Answer: total cost = 36/w + 36/l + 9lw
Step-by-step explanation:
The formula for determining the volume of the rectangular box is expressed as
Volume = lwh
Where lwh represents the length, width and height of the box respectively.
Since the volume of the box = 3cm³,then
lwh = 3
h = 3/lw
Since the box is open, the surface area would be
2lh + 2wh + lw
Given that the material for the sides of the box costs 6 per square meter, the total cost for the sides is
(2lh × 6) + (2wh × 6)
Substituting h = 3/lw into the above expression, it becomes.
(2l × 3/lw × 6) + (2w× 3/lw × 6)
= 36/w + 36/l
Since the material for the bottom costs 9per square meter, the total cost for the bottom is
9 × lw = 9lw
Therefore, the total cost of the box as a function of the length land width is
36/w + 36/l + 9lw
