14U Max/Min Word Problems
1) An isosceles triangle has two sides which are equal, and a base. The sides
that
√ are equal I call s and s; the base I call b. The area of such a triangle is
1
2
2
4 b 4s − b . If the perimeter of the triangle is 3 inches; what lengths should
s and b have, so that the area of the triangle is a maximum?.
a) Draw a diagram and label it with the variables.
b) Find the objective and the constraint equations.
c) Use the constraint equation to eliminate all but one variable in the objective
function.
d) Phrase the problem as a max/min problem on an interval.
e) Solve the max/min problem.
2) A box has a square base and top. It has a volume of 1000 f t3 . What
dimensions minimize the surface area? .
a) Draw a diagram and label it with the variables.
b) Find the objective and the constraint equations.
c) Use the constraint equation to eliminate all but one variable in the objective
function.
d) Phrase the problem as a max/min problem on an interval.
e) Solve the max/min problem.
3) A rectangle in inscribed is a unit circle: two sides are parallel to the x-axis;
the other two sides are parallel to the y-axis, and the corners of the rectangle
lie on the circle. What dimensions maximize the area of the rectangle?
a) Draw a diagram and label it with the variables.
b) Find the objective and the constraint equations.
c) Use the constraint equation to eliminate all but one variable in the objective
function.
d) Phrase the problem as a max/min problem on an interval.
e) Solve the max/min problem.
apparently I can't copy; it said 1/4 in the problem :(