SOLUTION: An artist is painting a supply of small paintings to sell at an arts festival. he can paint three landscapes per hour and two seascapes. He can frame five painting per hour. He

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Question 48955This question is from textbook finite mathematics
: An artist is painting a supply of small paintings to sell at an arts festival. he can paint three landscapes per hour and two seascapes. He can frame five painting per hour. He has 50 hours available for painting and 25 hours for framing. How many of each type of painting should he paint and frame in order to maximize the total value of the paintings. He receives $25 each for the landscapes and $30 each for the seascapes.
a. Max Value = $4,375 for 75 landscapes and 50 seascapes
b. Max Value = $3,375 for 75 landscapes and 50 seascapes
c. max Value = $4,375 for 50 landscapes and 75 seascapes
d. Max Value = $3,375 for 50 landscapes and 75 seascapes This question is from textbook finite mathematics

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
An artist is painting a supply of small paintings to sell at an arts festival. he can paint three landscapes(L) per hour and two seascapes(S). He can frame five painting per hour. He has 50 hours available for painting and 25 hours for framing. How many of each type of painting should he paint and frame in order to maximize the total value of the paintings. He receives $25 each for the landscapes and $30 each for the seascapes.
L... L.S. REQUIRE...........L/3 HRS.
S...S.S...REQUIRE...........S/2 HRS.
TOTAL HRS REQD FOR PAINTING=L/3 + S/2 <=50.....3L+2S<=300...............I
TOTAL PAINTINGS =L+S
TIME REQUIRED OR FRAMING=(L+S)/5<=25........L+S<=125................II
L>=0....AND.........S>=0
MONEY RECEIVED = M = 25L+30S...TO BE MAXIMUM..................III
DRAW LINES FOR EQN.I AND II TAKING EQUAL SIGN.
SO APPLICABLE VALUES FOR L AND S ARE BELOW THESE LINES TOWARDS ORIGIN.
THEY CUT AT L=50,S=75.
THE MONEY LINE WITH SLOPE =-30/25=-6/5....PASSING THROUGH POINT GIVES MAXIMUM INCOME,AS IF IT CROSSES THIS POINT IT WILL GO BEYOND APPLICABLE ZONE,MAHING DAYS INSUFFICIENT FOR FRAMING AND/OR PAINTING

MAXIMUM MONEY EARNED OULD BE
M=25*50+30*75=1250+2250=3500