A sketch artist sells on demand portraits and name doodles at the state fair. The artist has a personal maximum of 40 creations per day. With his current paper supply the artist is equipped to create up to 30 portraits and up to 20 name doodles. If the artists profit is $10 on each portrait and $20 on each name doodle, how many of each item should he aim to sell to maximize his profit?

profit will be maximized by making 20 doodles and 20 paintings = ($10 x 20) + ($20 x 20) = $600

Step-by-step explanation:

we have to maximize the following equation:

$10P + $20D

where:

P = number of portraits

D = number of doodles

the constraints are:

P + D ≤ 40

P ≤ 30

D ≤ 20

we do not need to use solver or any other type of linear programming tool to solve this, since profit will be maximized by making 20 doodles and 20 paintings = ($10 x 20) + ($20 x 20) = $600