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 $719 to buy chocolate (X) and strawberries (Y). The price of a chocolate is $83 and the price of a strawberry is $43.
Write Alice's budget constraint. Can he afford 6 chocolates and 6 strawberries at the same time?
Alice's budget constraint is
$$ 83 X + 43 Y \leq 719 $$In total, 6 chocolates and 6 strawberris costs Alice
$$ 83 \times 6 + 43 \times 6 = 756 $$No! Alice cannot afford 6 chocolate bars and 6 strawberries.