1. Identify the given from the statements.
• Let the side of the square base= s
• Height of the rectangular box be= h
,
• Given that :
s^2h = 20ft^3
solving for sh: s^2h = 20
s^2=20/h
s*s/s = 20/h /s
s = 20/hs
• Therefore sh = 20/s
Expandingthe given statements , we learn that :
• Material cost for base per square foot = 20 cents
,
• Material cost for sides per square foot = 18 cents
,
• Material cost for the top per square foot = 14 cents
2. Calculate Total cost
Total cost = {(s^2*20) + 4(sh)*18 +s^2*14}cents
= 20s^2 + 72*20/s + 14s^2
=34s^2 + 1440/s
• Expressing Total cost in terms of x , let s = x .
• Then Total cost (x) = 34x^2 +1440/x
2. Calculating the domain of TC(x) =34x^2 +1440/x
x <0 or x> 0
Domain (-∞;0) U(0;∞)