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 $678 to buy chocolate (X) and strawberries (Y). The price of a chocolate is $29 and the price of a strawberry is $63.
Write Alice's budget constraint. Can he afford 2 chocolates and 3 strawberries at the same time?
Alice's budget constraint is
$$ 29 X + 63 Y \leq 678 $$In total, 2 chocolates and 3 strawberris costs Alice
$$ 29 \times 2 + 63 \times 3 = 247 $$Yes! Alice can offord 2 chocolate bars and 3 strawberries.