text: please help with the calc problem!? answer to this calc problem: a river depth is d(x)=20x+10 and width is w(x)=10(x^2-8x+22) feet. if a dam cannot be more than 310 feet wide and 130 feet above the riverbedd and the top of the dam must be 20 feet above the present river surface, where can the dam be placed? d(x) = 20x + 10 ≤ 130 - 20 = 110 (as there must be 20 ft above the present river surface so 20x ≤ 100 x ≤ 5  w(x) = 10(x² - 8x + 22) ≤ 310 ie x² - 8x + 22 ≤ 31 so x² - 8x + 9 ≤ 0 ie (x - 9)(x + 1) ≤ 0 so -1 ≤ x ≤ 9 as x ≥ 0 (cannot have a negative depth or width) 0 ≤ x ≤ 9 so to satisfy both conditions, 0 ≤ x ≤ 5  what is maximum width in this range? well minimum occurs when x = -b/(2a) = 8/2 = 4 at endpoints when x = 0 w = 220ft when x = 5 w = 70ft so maximum width in this range is where the river is the shallowest. also minimum depth occurs at x = 0 when d = 10ft and maximum depth ocurs at x = 5 when d = 110ft  so now the choices need be made as the actual criteria being sought are not clearly spelt out.  in terms of straight economics it is probably wisest to have the almost least width and the maximum depth(at x = 5) but this is a guess.