outside perimeter is 2(4x+y) = 8x+2y
inside sections use 3y
cost is thus
c = 23(8x+2y) + 12(3y)
= 184x + 82y
Now, if the pens each occupy 14m^2, then y = 14/x, so
c = 184x + 82(14/x)
= 184x + 1148/x
minimum cost where dc/dx=0, or
184 - 1148/x^2 = 0
x = √(287/46) = 2.497
Now just figure y
A dog kennel with four pens is to be constructed. The pens will be surrounded by rectangular fence that costs $23 per meter. The rectangle is partioned into four pens of equal size with three partitions made of fence that costs $12 per meter. Each pen measures x meters wide by y meters long, as in the figure.What is the total cost of the fence?Suppose each pen must have 14 square meters of area. What should x and y be to minimize the cost of the fence?
1 answer
1 answer