A company makes two product,widgets and gadgets,which use the same materials in their production.Given a fixed amount of materials and labour,the company must decide how many widgets and gadgets to produce.If w widgets and g gadgets are produced,w and g must satisfy 9w^2+4g^2=18000.The graph of this equation for w≧0 and g≧0 is called the production possibilities curve,and a point(w,g) on this curve is a production schedule for the company.If a widget gives a profit of$3 and a gadget a profit of $4,find the production schedule that maximizes profit,using Lagrange multipliers.

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