Linear Programming WS #1
This is to help you get started on this worksheet since I am out with my
son. So take advantage of this help instead of just copying it down!
THINK about what is being done in the problem.
#1 The area of a parking lot is 600 square meters. A car requires 6 square
meters. A bus requires 30 square meters. The attendant can handle only
60 vehicles. If a car is charged $2.50 and a bus $7.50, how many of each
should be accepted to maximize income?
a) Identify whether you will maximize or minimize.
MAXIMIZE
b) define your variables.
Let c = Cars and b = Bus
c) write an objective function to be maximized or minimized.
P(c, b) = 2.50c + 7.50b
d) write a system of inequalities for the constraints.
e) graph the system of inequalities.
f)
find the coordinates of the vertices of the feasible region in the objective
function.
(0, 20)
(50, 10)
(60, 0)
g) substitute the coordinates of the vertices of the feasible region in the
objective function P(c, b) = 2.50c + 7.50b.
h) the greatest or least result to answer the question.
To maximize income there will need to be 50 cars and 10 buses in the
parking lot.
AGAIN!!!This is to help you get started on this worksheet since I am out with
my son. So take advantage of this help instead of just copying it down!
THINK about what is being done in the problem.
#2 The B & W Leather Company wants to add handmade belts and wallets to its product line.
Each belt nets the company $18 in profit, and each wallet nets $12. Both belts and wallets
require cutting and sewing. Belts require 2 hours of cutting time and 6 hours of sewing
time. Wallets require 3 hours of cutting time and 3 hours of sewing time. If the cutting
machine is available 12 hours a week and the sewing machine is available 18 hours per
week, what ratio of belts and wallets will produce the most profit within the constraints?
a)
b)
c)
d)
Identify whether you will maximize or minimize.
MAXIMIZE
define your variables.
Let b = belts and w = wallets
write an objective function to be maximized or minimized.
P(b, w) = 18b + 12w
write a system of inequalities for the constraints.
e) graph the system of inequalities.
f)
find the coordinates of the vertices of the feasible region in the objective
function.
(0, 4)
(1.5, 3)
(3, 0)
g) substitute the coordinates of the vertices of the feasible region in the
objective function P(b, w) = 18b + 12w.
h) the greatest or least result to answer the question.
There will need to be 1.5 belts and 3 wallets to maximize profit.
Assignment
• Finish the rest of Worksheet #2 in class and
what you do not finish is homework.
• WE WILL BE GRADING THIS IN CLASS FIRST
THING TOMORROW!!!!!