Example
Alice has $8 to buy chocolate (X) and strawberries (Y). So she can buy chocolate and strawberries, as long as she spends less than $8.
The price of a chocolate is $4. She finds strawberries for $2 each.
Her budget constraint is
$$4X + 2Y \leq 8$$A tiny bit of algebra gives
$$Y \leq - 2X + 4$$The budget constraint is the shaded area in the plot below
Question
Alice has $454 to buy chocolate (X) and strawberries (Y). The price of a chocolate is $53 and the price of a strawberry is $87.
Write Alice's budget constraint. Can he afford 6 chocolates and 2 strawberries at the same time?
Alice's budget constraint is
$$ 53 X + 87 Y \leq 454 $$In total, 6 chocolates and 2 strawberris costs Alice
$$ 53 \times 6 + 87 \times 2 = 492 $$No! Alice cannot afford 6 chocolate bars and 2 strawberries.