Constraints Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

medium
You have \50 to spend on notebooks (\3 each) and pens (\$2 each). Write the constraint inequality and find a valid combination.

Solution

  1. 1
    Let \(n\) = notebooks, \(p\) = pens.
  2. 2
    Constraint: \(3n + 2p \leq 50\).
  3. 3
    Also: \(n \geq 0\) and \(p \geq 0\) (non-negativity).
  4. 4
    Valid combo: \(n=10, p=10\): \(3(10)+2(10)=50 \leq 50\) โœ“

Answer

Constraint: \(3n + 2p \leq 50\); example: 10 notebooks and 10 pens
A constraint limits the feasible choices. Here the budget constraint \(3n + 2p \leq 50\) defines the region of possible purchases.

About Constraints

Conditions or restrictions that limit which values are allowed in a problem. Constraints narrow the set of possible solutions, such as 'x must be positive' or 'the total cannot exceed 100.'

Learn more about Constraints โ†’

More Constraints Examples

Example 2 hard

A farmer plants corn ([formula]150/acre profit) on at most 100 acres, with at least 20 acres of corn

Example 3 medium

A box must hold at least 10 items but no more than 25 items. Write this as a compound inequality and

Example 4 hard

A recipe needs at least 2 cups of flour and no more than 5 cups total of flour and sugar combined. I

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