Linear Programming: common misconceptions

If your child says… “The profit formula is the constraint.”

Ask together

Which describes the reward, and which describes the available space?

What’s true

The objective measures what you optimise; constraints limit your choices.

If your child says… “Meeting one restriction makes a choice allowed.”

Ask together

Do non-negative amounts guarantee that both drinks fit?

What’s true

Each allowed point must pass every restriction together.

If your child says… “The corner furthest right must earn most.”

Ask together

Which earns more here: four litres of the first drink or four of the second?

What’s true

For a nonempty, closed, bounded region, comparing every corner finds both extremes.

If your child says… “An endless region cannot have a minimum.”

Ask together

Where does the region with profit below two overlap the allowed region?

What’s true

Test below the smallest corner value for minima, above the largest for maxima.

If your child says… “Only the two corners give the maximum.”

Ask together

How much does the marked midpoint earn compared with either endpoint?

What’s true

Every point on the segment joining these optimal corners gives the same maximum.