Algebra 2A
Name _________________________________________
Notes 4 – 3 (D)
Linear Programming
Objective:
Define and solve application problems with a system of linear inequalities.
1.
George Jetson works at Spacely Sprockets producing two types of sprockets, Astro Sprockets
and Cosmic Sprockets. Mr. Spacely has already ordered 3 units of Astro Sprockets and 1 unit
of Cosmic Sprockets. Each unit of Astro Sprockets requires 1 batch of cogs and each unit of
Cosmic Sprockets requires 3 batches of cogs. George has 36 batches of cogs available but
knows that he can produce no more than 16 total units of sprockets each day.
a.
Write a system of inequalities to represent the constraints.
Astro Sprockets
x  ______
Cogs
_____ + _____  _____
Cosmic Sprockets
y  ______
Total per Day
_____ + _____  _____
b.
Graph the feasible region (graph the system).
c.
If Spacely Sprockets earns $323 profit on each unit of Astro Sprockets and $438 profit on each
unit of Cosmic Sprockets, write the objective function (profit function).
P = ______________________
d.
e.
Name the coordinates of the vertices for the feasible region and calculate the profit for each
vertex point.
_________
P = _________
_________
P = _________
_________
P = _________
_________
P = _________
George should produce _____ units of Astro Sprockets and _____ units of Cosmic Sprockets in
order to maximize profits for Mr. Spacely.
2.
Gibson Manufacturing produces gadgets with cords and cordless gadgets. They have already
received orders for 2 gadgets with cords and 4 cordless gadgets. Gadgets with cords require 2
widgets, while cordless gadgets require only 1 widget. However, gadgets with cords require
only 1 sprocket, while cordless gadgets require 2 sprockets. Gibson Manufacturing has 18
widgets and 24 sprockets on hand.
a.
Write a system of inequalities to represent the constraints.
Gadgets with Cords x  ______
Cordless Gadgets
y  ______
Widgets
_____ + _____  _____
Sprockets
_____ + _____  _____
b.
Graph the feasible region (graph the system).
c.
If they make $64 profit on gadgets with cords and $87 profit on cordless gadgets, write the
objective function (profit function).
P = ______________________
d.
e.
Name the coordinates of the vertices for the feasible region and calculate the profit for each
vertex point.
_________
P = _________
_________
P = _________
_________
P = _________
_________
P = _________
Gibson Manufacturing should produce _____ gadgets with cords and _____ cordless gadgets in
order to maximize their profits.
Algebra 2A
Name:
Worksheet 4 – 3 (D) : Linear Programming
1.
Ike’s Bikes manufactures both tricycles and bicycles. Their distributors have already placed
orders for 2 tricycles and 3 bicycles. Each tricycle requires 3 wheels and takes 1 hour to
manufacture. Each bicycle requires 2 wheels and takes 2 hours to manufacture. Ike’s Bikes
has 36 wheels in stock and has 20 hours to spend on the project.
a.
Write a system of inequalities to represent the constraints.
Tricycles
x  ______
Wheels
_____ + _____  _____
Bicycles
y  ______
Time
_____ + _____  _____
b.
Graph the feasible region (graph the system).
c.
If Ike’s Bikes makes $255 profit on each tricycle and $323 profit on each bicycle, write the
objective function (profit function).
P = ______________________
d.
e.
Name the coordinates of the vertices for the feasible region and calculate the profit for each
vertex point.
_________
P = _________
_________
P = _________
_________
P = _________
_________
P = _________
Ike’s Bikes should manufacture _____ tricycles and _____ bicycles in order to maximize their
profits.
2.
This week Color Blast paint manufacturers are producing two colors of paint, Spring Haze and
Emerald Isle. Their distributors have already ordered 2 batches of Spring Haze and 3 batches
of Emerald Isle. Each batch of Spring Haze requires 3 units of yellow dye and 1 unit of blue
dye. Each batch of Emerald Isle requires 2 units of yellow dye and 2 units of blue dye. They
have 30 units of yellow dye and 22 units of blue dye on hand.
a.
Write a system of inequalities to represent the constraints.
Spring Haze
x  ______
Yellow Dye
_____ + _____  _____
Emerald Isle
y  ______
Blue Dye
_____ + _____  _____
b.
Graph the feasible region (graph the system).
c.
If Color Blast makes $522 profit on each batch of Spring Haze and $614 profit on each batch of
Emerald Isle, write the objective function (profit function).
P = ______________________
d.
e.
Name the coordinates of the vertices for the feasible region and calculate the profit for each
vertex point.
_________
P = _________
_________
P = _________
_________
P = _________
_________
P = _________
Color Blast paint manufacturers should produce _____ batches of Spring Haze and _____
batches of Emerald Isle in order to maximize their profits.
3.
The Beadery produces beaded bracelets and necklaces. Their distributors have already
ordered 4 units of bracelets and 1 unit of necklaces. A unit of bracelets requires 1 carton of
beads, and a unit of necklaces requires 4 cartons of beads. The Beadery can produce no more
than 13 units total and has 28 cartons of beads in stock.
a.
Write a system of inequalities to represent the constraints.
Bracelets
x  ______
Beads
Necklaces
y  ______
Total per Day
_____ + _____  _____
_____ + _____  _____
b.
Graph the feasible region (graph the system).
c.
If they earn $311 profit on each unit of bracelets and $534 profit on each unit of necklaces, write
the objective function (profit function).
P = ______________________
d.
e.
Name the coordinates of the vertices for the feasible region and calculate the profit for each
vertex point.
_________
P = _________
_________
P = _________
_________
P = _________
_________
P = _________
The Beadery should produce _____ units of bracelets and _____ units of necklaces in order to
maximize their profits.