1. Use the cutting plane method to solve the following pure-integer programming
problem !
Maximize profit = 8 x1 + 6 x2
Subject to :
4 x1 + 6 x2  16
15 x1 + 3 x2  27
x1, x2 integers  0
2. Solve the following integer programming problem using the branch and bound
approach.
Maximize profit = 2 x1 + 3 x2
Subject to :
x1 + 3 x2  9
3 x1 + x2  7
x1 - x2  1
Where both x1 and x2 must be nonnegative integer values.
3. Student interprises sells two sizes of wall posters, a large 3- by -4 foot poster. The
profit earned from the sale of each large poster is $3; each smaller poster eranes $2.
The fiem although profitable, is not large ; it consist of one art student , Jan Meising,
at University of Kentucky. Because of her class room scheduled, Jan has the following
weekly constraints :
a. Up to three large posters can be sold ?
b. Up to five smaller posters can be sold ?
c. Up to 10 hours can be spent on posters durings the weeks, with each large
poster requiring 2 hours of work and each small one taking 1 hour. With the
semester almost over , Jan plans on taking a three month summer vacation to
England and doesn’t want to leave any unfinish poster behind. Find the integer
solution that will maximize the profit.