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 $336 to buy chocolate (X) and strawberries (Y). The price of a chocolate is $52 and the price of a strawberry is $12.
Write Alice's budget constraint. Can he afford 10 chocolates and 2 strawberries at the same time?
Alice's budget constraint is
$$ 52 X + 12 Y \leq 336 $$In total, 10 chocolates and 2 strawberris costs Alice
$$ 52 \times 10 + 12 \times 2 = 544 $$No! Alice cannot afford 10 chocolate bars and 2 strawberries.