Linear Programming Common Assessment (Ch. 3 & 4)
Name:_____________________
1. A tourist agency can sell up to 1200 travel packages for a Hawkeye football bowl game. The package includes
airfare, weekend accommodations, and the choice of two types of flights: a nonstop flight and a two-stop
flight. The nonstop flight can carry up to 150 passengers, and the two-stop flight can carry up to 100
passengers. The agency can locate no more than 10 planes for the travel packages. Each package with a
nonstop flight sells for $1200, and each two-stop flight package sells for $900. Assume that each plane carries
the maximum number of passengers.
a. Set-up a system of linear inequalities that represent the constraints of the problem.
{
b.
Find the feasible region by graphing the constraints. (May want to check your answers with a calculator
using INEQUALZ).
c.
Finding the corner points of the feasible region:
i. Change the inequalities to equations and then rewrite the equations in a matrix equation.
ii.
Find the points with either substitution OR elimination.
iii.
Find the points with determinants, an inverse matrix, or Gauss-Jordan (reduced row)
elimination.
Linear Programming Common Assessment (Ch. 3 & 4)
Name:_____________________
d.
Simplifications: Evaluate the objective function at all of the corner points and that maximizes the
revenue for the tourist agency, and find the maximum revenue.
e.
Discuss the domain and range of the system versus the domain and range of the problem.
Domain
Function
Story Problem
Range
Linear Programming Common Assessment (Ch. 3 & 4)
Name:_____________________
corner points and determine how many pounds of each blend should be prepared each day to maximize profit? What is
the maximum profit?
A store has requested a manufacturer to produce pants and sports jackets.
For materi als, the manufacturer has 750 m 2 of cotton textile and 1,000 m 2 of polyester.
Every pair of pants (1 unit) needs 1 m 2 of cotton and 2 m 2 of polyester. Every jacket needs
1.5 m 2 of cotton and 1 m 2 of pol yester.
The price of the pants is fi xed at $50 and the jacket, $40.
What is the number of pants and jackets that the manufacturer must give to the stores so
that these items obtai n a maximum sale?
1 Choose the unknowns.
x = number of pants
y = number of jackets
2 Write the objective function .
f(x,y)= 50x + 40y
3 Write the constraints as a system of inequaliti es.
To write the constraints, use a table:
pants jackets available
cotton
1
1,5
750
polyester
2
1
1,000
x + 1.5y ≤ 750
2x + y ≤ 1000
2x+3y ≤ 1500
Linear Programming Common Assessment (Ch. 3 & 4)
As
the
number
of
pants
and
jackets
Name:_____________________
are natural
numbers ,
there
are
two
constraints:
x ≥ 0
y ≥ 0
4 Find the set of feasible solutions that graphically represent the constraints.
Represent the constrai nts graphically.
As x ≥ 0 and y ≥ 0, work in the first quadrant.
Represent the straight lines from their points of intersecti on with the axes.
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