12. (a)Note that x2y51125, so y5}11x225}. Thenc55(x214xy)110xy55x2130xy55x2130x1}11x225}255x2133,750x21}ddcx}510x233,750x225}10(x32x23375)}The critical point occurs at x515. Since }ddcx},0 for 0 ,x ,15 and }ddcx}.0 for x .15, the critical pointcorresponds to the minimum cost. The values of xandyare x515 ft and y55 ft.(b)The material for the tank costs 5 dollars/sq ft and theexcavation charge is 10 dollars for each square foot ofthe cross-sectional area of one wall of the hole.13.Let xbe the height in inches of the printed area. Then thewidth of the printed area is }5x0}in. and the overall dimensions are x18 in. by }5x0}14 in. The amount ofpaper used is A(x)5(x18)1}5x0}14254x1821}40x0}in2. ThenA9(x)542400x225}4(x22x2100)}and the critical point(for x .0) occurs at x510. Since A9(x) ,0 for 0 ,x ,10 and A9(x) .0 for x .10, the critical pointcorresponds to the minimum amount of paper. Using x18 and }5x0}14 for x510, the overall dimensions are 18 in. high by 9 in. wide.
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