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 $309 to buy chocolate (X) and strawberries (Y). The price of a chocolate is $1 and the price of a strawberry is $75.
Write Alice's budget constraint. Can he afford 2 chocolates and 7 strawberries at the same time?
Alice's budget constraint is
$$ 1 X + 75 Y \leq 309 $$In total, 2 chocolates and 7 strawberris costs Alice
$$ 1 \times 2 + 75 \times 7 = 527 $$No! Alice cannot afford 2 chocolate bars and 7 strawberries.