A supermarket is to be designed as a rectangular building with a floor area of $10,000$ square feet. The front of the building will be mostly glass and will cost $$70$ per running foot for materials. The other three walls will be constructed of brick and cement block, at a cost of $$50$ per running foot. Ignore all other costs $($labor$,$ cost of foundation and roof, and the like$)$ and find the dimensions of the base of the building that will minimize the cost of the materials for the four walls of the building.

Let $y$ be the length of the side using glass and let $x$ be the length of a side that is adjacent to the glass side.

The objective equation is $C=x+y.$ The constraint equation is $xy=$

$($Do not include the $ symbol in your answer.$)$