Optimization worksheet with answers

Free printable Optimization worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
riverxxy

A farmer has 80 m of fencing to enclose a rectangular field along a straight river. No fence is needed along the river. Find the largest area A that can be enclosed.

80 m2x + y = 80
A = m²
2.Easy
x18 cm48 cmx

An open box is made from a rectangular sheet of cardboard 18 cm × 48 cm by cutting equal squares of side x from the four corners and folding up the sides. Find the largest possible volume V.

18 cm × 48 cm
V = cm³
3.Medium
rh

A closed cylindrical can (with a top and a bottom) must hold 400 cm³. The metal used is proportional to the total surface area. Find the radius r that uses the least material.

V = 400 cm³
r = cm
4.Medium
xhxno lid

An open box (no lid) with a square base must hold 62500 cm³. Use the least possible material, that is the smallest area of the base plus the four sides. Find the minimum surface area S.

V = 62500 cm³
S = cm²
5.Hard
qP(q)maximum

A small firm sells its product at a fixed market price of €65 per unit. Producing q units costs C(q) = 100 + 48q + 0.2q² euros. Find the maximum profit P.

p = €65C = 100 + 48q + 0.2q²
P = €
6.Hard
qP(q)maximum

A small firm sells its product at a fixed market price of €50 per unit. Producing q units costs C(q) = 5300 + 4q + 0.02q² euros. Find the maximum profit P.

p = €50C = 5300 + 4q + 0.02q²
P = €

Answer key

  1. 1. A = 800 m²
  2. 2. V = 1600 cm³
  3. 3. r = 3.993 cm
  4. 4. S = 7500 cm²
  5. 5. P = 261.3 €
  6. 6. P = 21150 €

Full step-by-step solutions: practise this topic on examproblems.com.