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Vincent Smudge, an avant-garde New York artist,creates “living sculpture” by sme

ID: 1111890 • Letter: V

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, T/3}, 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?

answer: 37.5

HOW TO SOLVE

Explanation / Answer

S would be maximized when L = T/3

50 x L + 10 x T = 3000 (Budget constraint)

50T/3 + 10T = 3000

T = 3000 x 3/80 = 112.5

L = 37.5

S = min (37.5,112.5/3) = 37.5