Problema Solution
yawaka manufactures motorcycles and bicycles. To stay in business, the number of bicycles cannot exceed five times the number of motorcycles. They lack the facilities to produce more than 90 motorcycles, or more than 200 bicycles, and the total production of motorcycles and bicycles cannot exceed 240. If yawaka makes $1010 on each motorcycle and $250 on each bicycle, how many of each should be made to maximize profit?
Answer provided by our tutors
let
m = the number of motorcycles produced
b = the number of bicycles produced
the number of bicycles cannot exceed five times the number of motorcycles
b <= 5m
they lack the facilities to produce more than 90 motorcycles, or more than 200 bicycles
m <= 90
b <= 200
he total production of motorcycles and bicycles cannot exceed 240
m + b <= 240
yawaka makes $1010 on each motorcycle and $250 on each bicycle
F(m, b) = 1010m + 250b
we need to find b and b so that F(m, b) has maximum
First draw the graph of the system of inequalities
b <= 5m
m <= 90
b <= 200
m + b <= 240
click here to see the graph
look at the graph and find the corner points - there are 4 corner points and calculate F(m ,b) for each point and find the maximum value (the biggest value for F)
(0, 0)
F(0, 0) = $0
(90, 0)
F(90, 0) = 1010*90 = $90,900
(90, 150)
F(90, 150) = 1010*90 + 250*150 = $128,400
(40, 200)
F(40, 200) = 1010*40 + 250*200 = $90,400
to maximize the profit the company should produce 90 motorcycles and 150 bicycles.