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 $812 to buy chocolate (X) and strawberries (Y). The price of a chocolate is $89 and the price of a strawberry is $50.
Write Alice's budget constraint. Can he afford 3 chocolates and 8 strawberries at the same time?
Alice's budget constraint is
$$ 89 X + 50 Y \leq 812 $$In total, 3 chocolates and 8 strawberris costs Alice
$$ 89 \times 3 + 50 \times 8 = 667 $$Yes! Alice can offord 3 chocolate bars and 8 strawberries.