## 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 $267 to buy chocolate (X) and strawberries (Y). The price of a chocolate is $38 and the price of a strawberry is $51.

Write Alice's budget constraint. Can he afford 5 chocolates and 8 strawberries at the same time?

Alice's budget constraint is

$$ 38 X + 51 Y \leq 267 $$In total, 5 chocolates and 8 strawberris costs Alice

$$ 38 \times 5 + 51 \times 8 = 598 $$No! Alice cannot afford 5 chocolate bars and 8 strawberries.