Problema Solution
A chainsaw requires 5 hours of assembly and a wood chipper 2 hours. A maximum of 20 hours of assembly time is available. the profit is $180 on a chainsaw and $220 on a chipper. How many of each should be assembled for maximum profit?
Answer provided by our tutors
let
c = the number of chainsaws assembled, c>0
w = the number of wood chippers assembled, w>0
a maximum of 20 hours of assembly time is available
5c + 2w <= 20
the profit is $180 on a chainsaw and $220 on a chipper thus the objective function is
F(c, w) = 180c + 220w
the constrains are
5c + 2w <= 20
w>=0
c>=0
click here to see the graph of the system of inequalities
the coordinates of the vertices of the feasible region are: (4, 0) and (0, 10)
lets apply the coordinates of the vertices to the objective function
F(4, 0) = 180*4 = $720
F(0, 10) = 220*10 = $2,200
we get the highest solution (maximum profit) for 0 chainsaws and 10 wood chippers.