Optimization problems

Answer Key - Grade 12 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   The area of Esme's garden bed is A(x) = −2x² + 24x square meters. At what x is A greatest?

   6
2. 2.

   The area of Jun's poster is P(x) = −3x² + 60x square inches. At what x is P greatest?

   10
3. 3.

   Kira tosses a beanbag; its height is h(x) = −5x² + 30x meters after x seconds. At what x is h greatest?

   3
4. 4.

   Milo has 40 m of fence for a rectangular pen along a barn wall, which forms one side. The two sides that touch it are x each. Which is the area?

   • A(x) = x(40 − x)
   • A(x) = 2x + (40 − 2x)
   • A(x) = x(40 − 2x)
5. 5.

   Noah has 64 m of fence for a rectangular pen along a riverbank, which forms one side. The two sides that touch it are x each. Which is the area?

   • A(x) = x(64 − x)
   • A(x) = 2x + (64 − 2x)
   • A(x) = x(64 − 2x)
6. 6.

   Ren has 50 m of fence for a rectangular pen along a long hedge, which forms one side. The two sides that touch it are w each. Which is the area?

   • A(w) = w(50 − 2w)
   • A(w) = 2w + (50 − 2w)
   • A(w) = w(50 − w)
7. 7.

   Zee has 36 m of fence for a rectangular pen along a school fence, which forms one side. The two sides that touch it are w each. Which is the area?

   • A(w) = w(36 − w)
   • A(w) = 2w + (36 − 2w)
   • A(w) = w(36 − 2w)
8. 8.

   Tala has 40 m of fence for a rectangular pen against a long wall, which forms one side. What is the largest area the pen can have, in m²?

   200
9. 9.

   Esme has 48 m of fence for a rectangular pen against a long wall, which forms one side. What is the largest area the pen can have, in m²?

   288
10. 10.

    Jun has 60 m of fence for a rectangular pen against a long wall, which forms one side. What is the largest area the pen can have, in m²?

    450