A fence is to enclose a rectangular area. One side is against a building so it needs no fence. This fencing costs $10/m. Inside the rectangular area there is a another fence at right angles to the building, costing$4/m. The total area enclosed is 12m^2. Find the dimensions for minimum cost. Include a second derivative test to show this is a minimum and include an answer with units and 3 sig. digits.

Im having problems figuring out how to solve this problem. Help would be greatly appreciated. Thanks!

2. Originally Posted by Hockey_Guy14
A fence is to enclose a rectangular area. One side is against a building so it needs no fence. This fencing costs $10/m. Inside the rectangular area there is a another fence at right angles to the building, costing$4/m. The total area enclosed is 12m^2. Find the dimensions for minimum cost. Include a second derivative test to show this is a minimum and include an answer with units and 3 sig. digits.

Im having problems figuring out how to solve this problem. Help would be greatly appreciated. Thanks!

let x = fence distances perpendicular to the bldg

y = fence distance parallel to the bldg

xy = 12

cost, C = 10(2x+y) + 4x

using the area equation, solve for one of the variables in terms of the other (either x or y, your choice) , then substitute into the cost equation to get cost in terms of a single variable ... then do the calculus.