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 $619 to buy chocolate (X) and strawberries (Y). The price of a chocolate is $25 and the price of a strawberry is $67.
Write Alice's budget constraint. Can he afford 7 chocolates and 6 strawberries at the same time?
Alice's budget constraint is
$$ 25 X + 67 Y \leq 619 $$In total, 7 chocolates and 6 strawberris costs Alice
$$ 25 \times 7 + 67 \times 6 = 577 $$Yes! Alice can offord 7 chocolate bars and 6 strawberries.