A homeowner plans to enclose a 200 square foot rectangular playground in his garden, with one side along the boundary of his property. His neighbor will pay for one third of the cost of materials on that side. Find the dimensions of the playground that will minimize the homeowner's total cost for materials. Follow the steps:

(a) express as a function of bothx andy, y being the width and x being the lengthC=______

(b) The condition thatx andy must satisfy isy=________

(c) Using the condition to replace ybyx inC ,Ccan then be expressed as a function ofx:C(x)= _______

(d) The domain ofC is _____

(e) The only critical number ofCin the domain isx=______. Classify the critical number as a relative maximum/minimum/or neither:

At the critical numberx=____, the second derivativeC'' () ispositive/negative/zero?

Therefore atx=_____ the function has a relative minimum/relative maximum/the second derivative test has no conclusion

(f) Finally, plugx=____into the condition ofx andy we obtainy=____.

Therefore the length and width of the playground that will minimize the homeowner's total cost for materials arex= ____ feet andy=____feet, with the side along the boundary of his property equals_______.