Question 84765This question is from textbook finite mathmatics
: 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 paintings an 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. Maximum value = $4,375 for 75 landscapes and 50 seascapes
B. Maximum value = $3,375 for 75 landscapes and 50 seascapes
C. Maximum value = $4,375 for 50 landscapes and 75 seascapes
D. Maximum value = $3,375 for 50 landscapes and 75 seascapes
This question is from textbook finite mathmatics
Answer by ankor@dixie-net.com(22740)   (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 per hour and two seascapes. He can frame five paintings an 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.
:
Let x = number of landscapes; y = number of seascapes
It takes 1/3 hr to paint one l.s
It takes 1/2 hr to paint one s.c.
:
Painting hours equation:
(1/3)x + (1/2)y = 50
Get rid of the denominators, multiply equation by 6 and you have:
2x + 3y = 300
:
Framing hours equation (it takes 1/5 of an hour to frame either one)
(1/5)x + 1/5(y) = 25
Get rid of the denominators, multiply equation by 5 and you have:
x + y = 125
y = (125 - x)
:
Substitute (125-x) for y in the painting hrs equation:
2x + 3(125-x) = 300
2x + 375 - 3x = 300
2x - 3x = 300 - 375
-x = -75
x = 75 landscapes
:
Solve for y using y = 125 - x
y = 125 - 75
y = 50 seascapes
:
Check our solutions using the original equation:
(1/3)x + (1/2)y = 50
(1/3)(75) + (1/2)(50) =
25 + 25 = 50
:
Find the value of this combination of paintings
75 * 25 = 1875
50 * 30 = 1500
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total $ = 3375
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