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 $724 to buy chocolate (X) and strawberries (Y). The price of a chocolate is $80 and the price of a strawberry is $36.
Write Alice's budget constraint. Can he afford 6 chocolates and 3 strawberries at the same time?
Alice's budget constraint is
$$ 80 X + 36 Y \leq 724 $$In total, 6 chocolates and 3 strawberris costs Alice
$$ 80 \times 6 + 36 \times 3 = 588 $$Yes! Alice can offord 6 chocolate bars and 3 strawberries.