Answer:
l = 20.5 cm
h = 17.5 cm
w = 9.5 cm
Step-by-step explanation:
Conditions
l+w =30 Solving for w 30 - l = w
h = l-3
V = l*w*h
Substituting in
V = l * (30-l) * (l-3)
= (30l-l^2) (l-3)
= 30 l^2 - l^3 - 90l + 3l^2
Combining like terms
Step-by-step solution
-l^3 + 33 l^2 - 90 l
To find the maximum we need to take the first derivative and then set it equal to zero
-3l^2 + 66l -90 = 0
Factor out a -3
-3 (l^2 -22l +30) =0
Using my calculator and the quadratic formula
l = 11 - sqrt(91)
l = 11 + sqrt(91)
l = 1.5 or 20.5 approximately
If l = 1. then
h= l-3 would be negative so
l = 20.5
h = l-3
h = 17.5 approximately
w = 30-l = 9.5 approximately