Problema Solution
a builder has 60 lots on which she can build one house per lot. she builds two types of houses, a colonial and a ranch. sales experience has told her she needs to build at least three times more ranchers than colonials. if she makes a profit of $5000 per colonial and $4500 for each rancher,how many of each should she build to maximize profit?
Answer provided by our tutors
let
c = the number of colonial houses, c>=0
r = the number of ranch houses, r>=0
a builder has 60 lots on which she can build one house per lot thus the total number of houses built must be not more then 60
c + r <= 60
she needs to build at least three times more ranchers than colonials
r >= 3c
she makes a profit of $5000 per colonial and $4500 for each rancher thus the total profit is the objective function
F(c, r) = 5000c + 4500r
lets graph the system of inequalities (the constrains)
c >=0
r >= 0
c + r <= 60
r >= 3c
click here to see the graph
the corner points are: (0, 0), (0, 60) and (15, 45)
F(0, 0) = 0
F(0, 60) = 4500*60 = $270,000.00
F(15, 45) = 15*5000 + 45*4500 = $277,500.00 is the maximum of the objective function
the maximum is achieved by building 15 colonial and 45 ranch houses.