Woolly Winker's peanut butter factory buys its nuts from two different suppliers, then produces peanut butter. Nuts from Farm X cost the factory $3 per pound, and nuts from Farm Y cost the factory $10 per pound.

The selling price (in dollars) for Wally Wonkee's peanut butter can be modeled by p(x,y)\displaystyle {p}{\left({x},{y}\right)} = 100−x−y\displaystyle {100}-{x}-{y} where x\displaystyle {x} is the demand for peanut butter made from Farm X's nuts and y\displaystyle {y} is the demand for peanut butter made from Farm Y's nuts. Assume that 0≤x,y\displaystyle {0}\le{x},{y}. Then Woolly Winker's max profit is attained when
x\displaystyle {x} =   pounds
y\displaystyle {y} =   pounds
The amount of the factory's maximum profit is $   .

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