1. ASSIGNMENT: MAXIMA AND MINIMA
CALCULUS
1. The sum of two positive numbers is 50. What are the numbers if their product is to be the
largest possible.
a. 24 and 26 b. 28 and 22 c. 25 and 25 d. 20 and 30
2. A farmer has enough money to build only 100 meters of fence. What are the dimensions of the
field he can enclose the maximum area?
a. 25 m x 25 m b. 15 m x 35 m c. 20 m x 30 m d. 22.5 m x 27.5 m

2. 3. Find the minimum amount of tin sheet (in square inches) that can be made into a closed
cylinder having a volume of 108 cubic inches.
a. 125.50 b. 127.50 c. 129.50 d. 123.50

3. 4. A poster is to contain 300 cm square of printed matter with margins of 10 cm at the top and
bottom and 5 cm at each side. Find the overall dimensions if the total area of the poster is
minimum.
a. 27.76 cm, 47.8 cm c. 22.24 cm, 44.5 cm
b. 20.45 cm, 35.6 cm d. 22.55 cm, 46.7 cm

4. 5. A Norman window is the shape of a rectangle surmounted by a semi-circle. What is the ratio of
the width of the rectangle to the total height so that it will yield a window admitting the most
light for a given perimeter.
a. A b. ½ c. 2 d. 2/3
6. The cost C of a product is a function of the quantity x of the product: C(x)=x2 – 4000x + 50. Find
the quantity for which the cost is minimum.
a. 1000 b. 1500 c. 2000 d. 3000

5. 7. An open top rectangular tank with square bases is to have a volume of 10 cubic meters. The
materials for its bottom is to cost P15 per square meter and that for the sides, P6 per square
meter. Find the most economical dimensions for the tank.
a. 1.5 m x 1.5 m x 4.4 m
b. 2 m x 2m x 2.5 m
c. 4m x 4m x 0.6 m
d. 3m x 3m x 1.1m

6. 8. Given a cone of diameter x and altitude h. What percent is the volume of the largest cylinder
which can be inscribed in the cone to the volume of the cone?
a. 44% b. 46% c. 56% d. 65%