A cobb douglas production function for a new company is given by F(x,y)=50x3/5y2/5. Where x represents the units of labor and y represents the units of capital. Suppose the units of labor and the capital cost is $200 and $100 each respectively and the budget constraint is $30,000. Find the maximum production level for this manufacturer.
"\\frac{\\varDelta L}{\\varDelta x}=30(\\frac{y}{x})^{\\frac{2}{5}}-200\\lambda"
"\\frac{\\varDelta L}{\\varDelta y}=20(\\frac{x}{y})^{\\frac{3}{5}}-100\\lambda"
"200x+100y=30000"
"x=109"
"y=82"
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