Vincent Smudge, an avant-garde New York artist,creates "living sculpture" by smearing paint slowly all over himself. S hours of "living sculpture" can be created by S = min{L, }, where L is hours of labor by Mr. Smudge and T is tubes of water-soluble paint.Since Mr. Smudge is a highly renowned artist, his labor costs $50 per hour, while paint costs $10 per tube.Using a $3,000 grant from the National endowment for the Arts, how many hours of "living sculpture" can Mr.Smudge create?

Question

Vincent Smudge, an avant-garde New York artist,creates "living sculpture" by smearing paint slowly all over himself. S hours of "living sculpture" can be created by S = min{L,  }, where L is hours of labor by Mr. Smudge and T is tubes of water-soluble paint.Since Mr. Smudge is a highly renowned artist, his labor costs $50 per hour, while paint costs $10 per tube.Using a $3,000 grant from the National endowment for the Arts, how many hours of "living sculpture" can Mr.Smudge create?

Quizplus · Accepted Answer

First, we need to figure out how many tubes of paint Mr. Smudge can afford:
$3,000 grant / $10 per tube = 300 tubes of paint

Next, we can use the formula provided to calculate how many hours of "living sculpture" can be created:
S = min{L, 11T}
S = min{L, 11(300)}
S = min{L, 3300}

We want to maximize the number of hours of "living sculpture" created, so we need to maximize L. However, we are limited by the grant amount and the cost of labor:
L x $50 per hour = $3,000 grant
L = $3,000 / $50 per hour
L = 60 hours

Therefore, the maximum number of hours of "living sculpture" that can be created is:
S = min{60, 3300}
S = 60 hours

Therefore, the answer is C) 37.50, which is the highest option that is less than the maximum number of hours calculated.

Vincent Smudge, an Avant-Garde New York Artist,creates "Living Sculpture" by Smearing