a tank with a rectangular base and rectangular sides is to be open at the top
Answers
The question is incomplete, here is the complete question.
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. if building the tank costs $10 per square meter for the base and $5 per square meter for the sides, what is the cost of the least expensive tank?
Answer:
w = 4
36 = l * 4 * h
9 = l * h
9/h = l
cost = (10 * l * w) + 2 * (5 * h * w) + 2 * (5 * l * h)
= 10lw + 10hw + 10lh
= 40l + 40h + 10lh
= 40(9/h) + 40h + 10h(9/h)
= 360/h + 40h +90
take the derivative of the equation to find where cost is at a minimum (cost' = 0)
cost' = -360*h^-2 +40
0 = -360*h^-2 +40
-40 = -360h^-2
1/9 = h^-2
+/- 1/3 = h^-1
+/- 3 = h
h cannot be negative as it is a measure of length so,
h=3
9/h = l
9/3 = l
3 =l
cost = (10 * l * w) + 2 * (5 * h * w) + 2 * (5 * l * h)
= (10 * 3 * 4) + 2 * (5 * 3 * 4) + 2 * (5 * 3 * 3)
= 120 + 120 + 90
= $330