1.) Find the point on the line -4x + 3y - 6 =0 which is closest to the point (1, -3).
2.) The manager of a large apartment complex knows from experience that 110 units will be occupied if the rent is 448 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 8 dollar increase in rent. Similarly, one additional unit will be occupied for each 8 dollar decrease in rent. What rent should the manager charge to maximize revenue?
2.) The manager of a large apartment complex knows from experience that 110 units will be occupied if the rent is 448 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 8 dollar increase in rent. Similarly, one additional unit will be occupied for each 8 dollar decrease in rent. What rent should the manager charge to maximize revenue?
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1. you have y = [4/3] x + 2 , slope is 4/3---> slope of a perpendicular line is - 3/4 and
thus the line through (1 , - 3 ) is y = ( - 3 / 4 ) x + 3/4 + 3 ,
now set the y values = and solve for x , then y
#2. Let x = change in units , then R = [units rented] [ cost per unit ]
R = [ 110 + x ] [ 448 - 8x ]...this is a quadratic and you certainly can find the high point
remember to ' complete the square ' { unless you have had some calculus }
thus the line through (1 , - 3 ) is y = ( - 3 / 4 ) x + 3/4 + 3 ,
now set the y values = and solve for x , then y
#2. Let x = change in units , then R = [units rented] [ cost per unit ]
R = [ 110 + x ] [ 448 - 8x ]...this is a quadratic and you certainly can find the high point
remember to ' complete the square ' { unless you have had some calculus }