IE400-STUDY SET-1
Spring 2017
1. Weenies and Buns is a food processing plant which manufactures hot dogs and hot dog buns.
They grind their own flour for the hot dog buns at a maximum rate of 200 pounds per week. Each
hot dog bun requires 0.1 pound of flour. They currently have a contract with Pigland, Inc., which
specifies that a delivery of 800 pounds of pork product is delivered every Monday. Each hot dog
requires 0.25 pound of pork product. All the other ingredients in the hot dogs and hot dog buns
are in plentiful supply. Finally, the labor force at Weenies and Buns consists of 5 employees
working full time (40 hours per week each). Each hot dog requires 3 minutes of labor, and each
hot dog bun requires 2 minutes of labor. Each hot dog yields a profit of $0.20, and each bun
yields a profit of $0.10. Weenies and Buns would like to know how many hot dogs and how
many hot dog buns they should produce each week so as to achieve the highest possible profit.
(a) Formulate a linear programming model for this problem.
(b) Use the graphical method to solve this model.
2. Consider the following portfolio problem. The available money for the investment is
$50,000,000. There are five loans and the risk and return values of each loan are shown in the
table:
Loan/Investment
Return(%)
Risk
Mortgage 1
9
3
Mortgage 2
12
6
Personal Loans
15
8
Commercial Loans
8
2
Government securities
6
1
Any uninvested money goes into a savings account with no risk and 3% return. The money to be
invested should be allocated as follows:
- Have an average risk of no more than 5 (all averages and fractions taken over the invested
money (not over the saving account)).
- Invest at least 20% in commercial loans.
- The amount in second mortgages and personal loans combined should be no higher than the
amount in first mortgages.
Formulate the LP problem to maximize the average return per dollar.
3. Solve the following LP problems by using graphical method and determine whether LP is
unique optimal,alternative optimal,infeasible,unbounded.
(a) Max Z= 8x1+4x2
subject to
2x1+ x2
≤4
2x1+ 4x2
≤ 6
and
x1≥ 0, x2≥ 0
(b) Min Z= -2x1-x2
subject to
3x1+ x2
x1 - x2
≤6
≤ 2
-x2 ≥ -3
and
x1≥ 0, x2≥ 0
(c) Max Z= 2x1+x2
subject to
x2
≤ 10
2x1+5x2
≤ 60
x1 + x2
≤ 18
3x1+ x2
≤ 44
and
x1≥ 0, x2≥ 0
(d) Max Z= 4x1+8x2
subject to
2x1 + 2x2 ≤ 10
x1 - x2
≤ -8
and
x1≥ 0, x2≥ 0
(e) Min Z= -x1-x2
subject to
8x1 + 6x2 ≥ 24
4x1 + 6x2 ≥-12
2x2 ≥ 4
and
x1≥ 0, x2≥ 0