Optimization Quiz

Name: ______________________   Date: __________   Score: ____ / 10

10 questions. Calculator allowed. Show your working. steplyclass.com/calculus-1/optimization/quiz/

1. 1

   Two positive numbers multiply to 64. Find the smallest possible sum.
   1. A) 16
   2. B) 1
   3. C) 64

2. 2

   Two positive numbers have a product of 49. Find the smallest possible sum.

   Answer: ____________________

3. 3

   A rectangle has an area of 100 cm². Find the smallest perimeter.
   1. A) 2 cm
   2. B) 100 cm
   3. C) 40 cm
   4. D) 200 cm

4. 4

   A rectangular garden of 50 m² is fenced on three sides. A wall is the fourth side. Find the least fencing needed.

   Answer: ____________________

5. 5

   A rectangular pen of 72 ft² is fenced on three sides. A barn is the fourth side. Find the least fencing needed.
   1. A) 24 ft
   2. B) 72 ft
   3. C) 2 ft
   4. D) 36 ft

6. 6

   A shop sells 300 cakes a day at $5 each. For every $1 it adds to the price, it sells 20 fewer cakes. What price gives the most money?

   Answer: ____________________

7. 7

   A square sheet of card is 12 cm by 12 cm. A square is cut from each corner and the sides are folded up to make an open box. Find the largest volume.
   1. A) 128 cm³
   2. B) 0 cm³
   3. C) 6 cm³

8. 8

   A square sheet of metal is 18 cm by 18 cm. A square is cut from each corner and the sides are folded up to make an open box. Find the largest volume.

   Answer: ____________________

9. 9

   An open box with a square base must hold 32 cm³. Find the least material needed.
   1. A) 32 cm²
   2. B) 4 cm²
   3. C) 48 cm²
   4. D) 128 cm²

10. 10

    An open box with a square base must hold 108 cm³. Find the least material needed.

    Answer: ____________________