minimizing the cost of diminsions

[jessica87689]

A rectangular enclosure must have one side of wood costing $8 per ft and the other three sides of chain link costing $4 per ft. The area enclosed is to be 15000 square feet. Find the dimensions that will minimize the cost. What is the cost?

okay, i started on this one, but i know either one or both of my equations is wrong. i know how to do this with three sides, but not four with three different costs.
anyways, heres what i've tried
objective function : 2x + 2y = P
subject to xy = 15000

minimize p = 2x + 2y subject to xy=15000 , x >(or equal to) 0 , y > (or equal to) 0

x = 15000/y
p = 2(15000/y)+ 2y
P= (30000/y ) + 2y

x > (or equal to) 0
so
30000/y > (or equal to) 0

but then you mutiply out y and end up with 30000 is greater than or equal to 0... and that cant be right
so either one or both of my equations are wrong and i cant seem to figure it out.

 

[fasteddie65]

A rectangular enclosure must have one side of wood costing $8 per ft and the other three sides of chain link costing $4 per ft. The area enclosed is to be 15000 square feet. Find the dimensions that will minimize the cost. What is the cost?

okay, i started on this one, but i know either one or both of my equations is wrong. i know how to do this with three sides, but not four with three different costs.
anyways, heres what i've tried
objective function : 2x + 2y = P
subject to xy = 15000

minimize p = 2x + 2y subject to xy=15000 , x >(or equal to) 0 , y > (or equal to) 0

x = 15000/y
p = 2(15000/y)+ 2y
P= (30000/y ) + 2y

x > (or equal to) 0
so
30000/y > (or equal to) 0

but then you mutiply out y and end up with 30000 is greater than or equal to 0... and that cant be right
so either one or both of my equations are wrong and i cant seem to figure it out.

The problem states that three sides cost $4 and one side $8.
4(2x + y) + 8y = C would be an equation for the total cost.

The area 15000 = xy, so your second equation seems correct.