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, T/5}, 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 $200 per hour, while paint costs $40 per tube.Using a $10,000 grant from the National Endowment for the Arts, how many hours of "living sculpture" can Mr.Smudge create?
A)1,666.67
B)48.08
C)41.67
D)25
E)8,333.33

Question

Quizplus · Accepted Answer

To maximize S, we need to balance the cost of labor and paint. With a $10,000 budget, if L hours of labor costs $200L and T tubes of paint cost $40T, then 200L + 40T = 10,000. Solving for maximum S, we find S = min{L, T/5}. By setting L = T/5, we find L = 25, which is the maximum hours of "living sculpture" possible.

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