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 $300 to buy chocolate (X) and strawberries (Y). The price of a chocolate is $9 and the price of a strawberry is $44.
Write Alice's budget constraint. Can he afford 9 chocolates and 5 strawberries at the same time?
Alice's budget constraint is
$$ 9 X + 44 Y \leq 300 $$In total, 9 chocolates and 5 strawberris costs Alice
$$ 9 \times 9 + 44 \times 5 = 301 $$No! Alice cannot afford 9 chocolate bars and 5 strawberries.