Posted by Caitlin on Tuesday, June 5, 2012 at 8:53pm.
top and bottom are w by w
height is h
324 = w^2 h so h = 324/w^2
Cost = 6 w^2 + 4 w h
= 6 w^2 + 4 w (324/w^2)
= 6 w^2 + 1296/w
dC/dw = 0 for min = 12 w -1296/w^2
0 = 12 w^3 - 1296
w^3 = 108
w = 4.76
h = 14.3
Are you sure about the 4w (324/w^2)?
Shouldn't it be 8w (324/w^2), since you are multiplying the four sides by the cost of $2 per square foot?
Yes, you're right.
If we proceed with
Cost = 6 w^2 + 8 w h
we get:
w=6 and h=9.
Related Questions
Calc - A rectangular box, with a square base and open at the top is to be ...
CALC - An open box is to be constructed so that the length of the base is 4 ...
calc - a closed box has a base twice as long as it is wide.if its volume is 100 ...
calculus - This is problem 16 Section 4.6 page 246. A closed box with square ...
AP Calculus - A cardboard box of 108in cubed volume with a square base and no ...
calculus - An open box is to be constructed so that the length of the base is 4 ...
Calculus - A box is constructed out of two different types of metal. The metal ...
calculus - A box is constructed out of two different types of metal. The metal ...
Math Calc - If 1500 square centimeters of material is available to make a box ...
maxima/minima problems - A regular box is open at the top and has a square base...
For Further Reading
