Question
An open rectangular tank (no top) with volume 11 cubic meters has a square base. The base has side x m. Write an equation for the surface area of the tank as a function of the length x.
Surface Area = ?
b. The base costs 1.1 cents/square m and the sides cost 1.6 cents/square m. Write an expression for the cost as a function of x.
Cost = ?
c. The value of x to achieve minimum cost is
x = ?
Surface Area = ?
b. The base costs 1.1 cents/square m and the sides cost 1.6 cents/square m. Write an expression for the cost as a function of x.
Cost = ?
c. The value of x to achieve minimum cost is
x = ?
Answers
If the base is square of area x^2, then the height is 11/x^2
area = x^2 + 4(11/x^2)
cost = 1.1 x^2 + (1.6)(4)(11/x^2) = 1.1x^2 + 70.4/x^2
dc/dx = 2.2x - 140.8/x^3 = 2.2x(x^4-64)/x^3
dc/dx=0 when x=2√2
area = x^2 + 4(11/x^2)
cost = 1.1 x^2 + (1.6)(4)(11/x^2) = 1.1x^2 + 70.4/x^2
dc/dx = 2.2x - 140.8/x^3 = 2.2x(x^4-64)/x^3
dc/dx=0 when x=2√2