Calculus I
Section 4.7B – Optimization (Cost, Inscribed, Distance)
1. A rectangular area of 4800 square ft. is to be fenced off using two types of fencing. One type costs $4
per foot and the other costs $6 per foot. Opposite sides of the rectangle use the same type of fencing.
How much of each type should be used in order to minimize the cost of the fencing?
2. A landscape architect plans to enclose a 3000 square foot rectangular region in a botanical garden.
She will use shrubs costing $25 per foot along three sides and fencing costing $10 per foot along the
fourth side. Find the minimum total cost.
3. A closed rectangular box with a square base is to have a volume of 2250 cubic inches. The material
for the top and bottom of the box will cost $2 per square inch, and the material for the sides will cost
$3 per square inch. Find the dimensions of the container of least cost.
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Calculus I
Section 4.7B – Optimization (Cost, Inscribed, Distance)
4. A cylindrical can (closed at the top) holds 750 ml of liquid. Find the height and radius of the can that
will minimize the amount of material used in making the can. (Use the formula for surface area of a
cylinder in the front cover of the textbook.)
5. Find the radius of the largest right circular cylinder that can be inscribed in a sphere with R = 100.
6. Find the height and radius of the largest cylinder that can be inscribed in a sphere of radius R = 30.
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Calculus I
Section 4.7B – Optimization (Cost, Inscribed, Distance)
7. A rectangle is to be inscribed in a semicircle of radius 2. What are the dimensions of the rectangle
with largest area?
8. Find the point on the graph of y = x2 that is closest to the point (3,0).
9. What points on the ellipse x2 + 4y2 = 8 are nearest the point (1,0)?
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