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# A firm uses wool and cotton fiber to produce cloth. The amount of cloth produced is given by $Q(x, y)=x y-x-y+1$, where $x$ is the number of pounds of wool, $y$ is the number of pounds of cotton, and $x>1$ and $y>1$. If wool costs $p$ dollars per pound, cotton costs $q$ dollars per pound, and the firm can spend $B$ dollars on material, what should the mix of cotton and wool be to produce the most cloth?

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The amount of cloth produced is described by the function $Q(x,y)=xy-x-y+1$.

The cost function is given by $g(x,y)=px+qy$. In fact, the cost of wool is $p$ dollars per pound; and cotton, $q$ dollars per pound. Since the firm can spend $B$ dollars then $g(x,y)=B$.

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