Posted by john on Monday, December 12, 2011 at 1:09am.
A tank with a rectangular base and rectangular sides is to be open at the top. It is to be constructed so that its width is 4 meters and its volume is 36 cubic meters. Building the tank costs $10 per square meter for the base and $5 per square meter for the sides.
a) Write a function C, the cost of constructing the described tank as a function of l(the length) and h(the height).
b) Write a function C, the cost of constructing the described tank as a function of a single variable.
c) What is the cost of the least expensive tank? (show all work)

calculus  Reiny, Monday, December 12, 2011 at 8:59am
let its length be l m
and its height by h m
volume = 4lh
but 4lh = 36
h = 9/l
a) cost = 10(4l) + 5(2lh) + 5(8h)
= 40l + 10lh + 40h
b) cost = 10(4l) + 5(2l)(9/l) + 40(9/l
= 40l + 90 + 360/l ,where l ≠ 0
c) d(cost)/dl = 40 + 0  360/l^2 = 0 for a min of cost
40 = 360/l^2
l^2 = 9
l = √9 = 3
when l = 3, h = 9/3 = 3
dimensions for min cost = 3by4 for the base and a height of 3
cost = 330.00
test: take a value slightly higher and lower than l = 3
l = 3.1, cost = 330.13 , higher
l = 2.9 , cost = 330.14 , higher
answer looks good
Answer This Question
Related Questions
 Calculus AB/AP  A tank with a rectangular base and rectangular sides is to be ...
 math  A box with a rectangular base and rectangular sides is to be open at the ...
 Calculus  A rectangular storage container with an open top is to have a volume ...
 Math  An open rectangular tank (no top) with volume 11 cubic meters has a ...
 Calc 1 (Optomization)  A rectangular storage container with an open top is to ...
 AP CALCULUS!!! HELPP  related rates: the base of a pyramidshaped tank is a ...
 AP CALCULUS!! HELPPP URGENT  related rates: the base of a pyramidshaped tank ...
 Calculus  A holding pen for fish is to be made in the form of a rectangular ...
 Calculus  A rectangular tank with a square? base, an open? top, and a volume of...
 MATH!!  A fish tank with a rectangular base has a volume of 3,360 cubic inches...
More Related Questions