The Keyesport Quarry has two different pits from which it obtains rock. The rock is run through a crusher to produce two products: concrete grade stone and road surface chat. Each ton of rock from the South pit converts into $0\mathrm{.}75$ tons of stone and $0\mathrm{.}25$ tons of chat when crushed. Rock from the North pit is of different quality. When it is crushed, it produces a $50-50$ split of stone and chat. The Quarry has contracts for $60$ tons of stone and $40$ tons of chat this planning period. The cost per ton of extracting and crushing rock from the South pit is $1\mathrm{.}6$ times as costly as from the North pit.