What You Need to Know

Optimisation means finding the greatest or least value of a function within given constraints

Constraints are conditions that restrict the possible values of variables

Linear programming uses straight-line constraints to find optimal solutions on a feasible region

The optimal solution in linear programming always occurs at a vertex of the feasible region

In single-variable optimisation, setting the derivative to zero locates stationary points

Key Vocabulary

The process of finding maximum or minimum values of an objective function

A restriction or condition that limits the possible solutions to a problem

The set of all points that satisfy all constraints in a linear programming problem

The function to be maximised or minimised in an optimisation problem

Select the correct answer for each question. Click "Check Answer" to see if you are right.

Question 1

A farmer has 60 m of fencing to enclose a rectangular pen along a wall (no fencing needed on the wall side). What width maximises the area?

20 m 30 m 15 m 10 m

Question 2

In a linear programming problem, where is the optimal solution always found?

At the origin At the midpoint of the feasible region Along the largest constraint line At a vertex (corner point) of the feasible region

Question 3

A box with a square base has no lid and uses 300 cm^2 of material. If the base side is x, which expression gives the height h?

h = (300 - x^2)/(4x) h = 300/(4x) h = 300/x^2 h = x/4