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
The question is for any rational function. I give one example in picture below. There we can see that first part of the "rule" is true. we indeed have vertical asymptotes at every x value where denominator is zero in this case x = 3 and x = 1. but second part of the rule is not true. we can see that if we inverse x ( we have factor that looks like a - x we get positive function between asymptotes.
P(black socks): 24/42 or 12/21 P(black socks without replacing): 23/41. As a result, the probability of randomly picking 2 black socks, without replacement, from the basket is 12/21×23/41=276/861 or 32%. Hope it help!
