The process of making cocoa powder is actually a joint costing process. Specifically, the cocoa beans are processed to produce cocoa butter, cocoa powder, and waste. Suppose that a company processes cocoa beans and has $$250$ of costs to purchase the beans and separate the beans into butter, powder, and waste. After separating the products, the company has $40$ pounds of cocoa butter, $35$ pounds of cocoa powder, and $15$ pounds of waste. At that point, the company pays a total of $$179$ to process the butter, $$143$ to process the powder, and $$96$ to dispose of the waste. The butter then sells for $$509$ and the powder sells for $$487.$ The waste is not sold. What is the total cost of the butter if the company allocates joint costs based on weight? Round your answer to the nearest whole dollar. Note that for this problem and related problems, all costs and prices are given as total numbers, not per$-$pound numbers.