Question

An open box is to contain a volume of 3 cubic meters. Given that the material forthe sides of the box costs 6 per square meter and the material for the bottom costs 9per square meter, express the total costCof the box as a function of the lengthlandwidthw.

Answer 1

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