A mining company has available a total of 100 square miles of mining sites and considering the use of two mining techniques: heap leaching and vat leaching. For each square mile of land, heap leaching technique can have a daily production of 3 tons of rare earth oxide per square miles but it also creates 8 tons of polluted wastewater and requires 10 extraction machines. On the other hand, vat leaching technique produces 5 tons of rare earth oxide per square miles per day while creating 17 tons of polluted wastewater and requiring 20 extraction machines. There are 100 machines available and due to environmental regulations, the amount of polluted wastewater must be at most 90 tons daily. Find the proportion of lands that use each mining technique in order to maximize the daily production of rare earth oxide.