Question

Assume that relative maximum and minimum values are absolute maximum and minimum values. Safe Shades produces two kinds of sunglasses; one kind sells for 17 dollars, and the other for 21dollars The total revenue in thousands of dollars from the sale of $x$ thousand sunglasses at 17 dollars each and $y$ thousand at 21 dollars each is given by $R(x, y)=17 x+21 y$ The company determines that the total cost, in thousands of dollars, of producing $x$ thousand of the 17 dollars sunglasses and $y$ thousand of the 21 dollars sunglasses is given by $$C(x, y)=4 x^{2}-4 x y+2 y^{2}-11 x+25 y-3$$ Find the number of each type of sunglasses that must be produced and sold in order to maximize profit.

          Assume that relative maximum and minimum values are absolute maximum and minimum values.
Safe Shades produces two kinds of sunglasses; one kind sells for 17 dollars, and the other for 21dollars  The total revenue in thousands of dollars from the sale of $x$ thousand sunglasses at 17 dollars  each and $y$ thousand at 21 dollars each is given by $R(x, y)=17 x+21 y$ The company determines that the total cost, in thousands of dollars, of producing $x$ thousand of the 17 dollars sunglasses and $y$ thousand of the 21 dollars  sunglasses is given by $$C(x, y)=4 x^{2}-4 x y+2 y^{2}-11 x+25 y-3$$ Find the number of each type of sunglasses that must be produced and sold in order to maximize profit.

Added by Thomas S.

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