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.

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Name: ____________________ Date: ____________

1.Easy

An open box is made from a rectangular sheet of cardboard 15 cm × 24 cm by cutting equal squares of side x from the four corners and folding up the sides. Find the cut x that gives the largest volume.

15 cm × 24 cm

x = cm

2.Easy

A rectangular pen is fenced with 120 m of fencing and divided into two parts by one extra fence parallel to the sides of length x (three fences of length x and two of length y in total). Find the largest total area A that can be enclosed.

120 m3x + 2y = 120

A = m²

3.Medium

A closed cylindrical can (with a top and a bottom) must hold 1000 cm³. The metal used is proportional to the total surface area. Find the radius r that uses the least material.

V = 1000 cm³

r = cm

4.Medium

A closed cylindrical can (with a top and a bottom) must hold 1000 cm³. The metal used is proportional to the total surface area. Find the height h of the can that uses the least material.

V = 1000 cm³

h = cm

5.Hard

A company sells q units per week. The price at which it can sell them is p = 90 − 1q euros per unit, and the cost is C(q) = 500 + 35q euros. Find the maximum weekly profit P.

p = 90 − 1qC = 500 + 35q

P = €

6.Hard

A company sells q units per week. The price at which it can sell them is p = 160 − 0.5q euros per unit, and the cost is C(q) = 3600 + 40q euros. Find the maximum weekly profit P.

p = 160 − 0.5qC = 3600 + 40q

P = €

Answer key

1. x = 3 cm
2. A = 600 m²
3. r = 5.419 cm
4. h = 10.84 cm
5. P = 256.3 €
6. P = 3600 €

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