Correct question is;
A rectangular storage container with an open top has a volume of 20 m³. The length of its base is twice its width. Material for the base costs $20 per square meter; material for the sides costs $8 per square meter. Express the cost of materials as a function of the width of the base.
Answer:
C = 40W² + 480/W
Explanation:
We are given;
Volume; V = 20 m³
Length of base is L
Width of base is W
We are told L = 2W
Formula for volume of a cuboid = LWH
Thus;
20 = 2W × W × H
20 = 2W²H
H = 10/W²
Now, we are given cost of materials for base and sides.
Formula for base area = LW = 2W²
Formula for side areas = 2(LH) + 2(WH) = 2(2WH) + 2WH = 6WH = 6W(10/W²) = 60/W
Cost per Sq.m of base = $20.
Thus, base cost = 20(2W²) = 40W²
Cost per Sq.m of sides = 8(60/W)
Thus,sides cost = 480/W
Total cost of sides and base is;
C = 40W² + 480/W