MSCI 316 Practice problems Spring 02 Exam #2
1) Use the graphical method to solve the linear
problem, where x1 = Alaska oil and x2 = Arabian
MINIMIZE 2x1 + 7x2
subject to constraints
(1)
4x1 + 3x2 >
(2)
x1 + x2 <
(3)
x1 + 3x2 >
x1
>
x2 >
(a) List feasible corner points
(b) Optimal solution:
(c) Minimum cost =
programming
oil
96
50
60
0
0
2) Do sensitivity analysis for this linear programming problem:
MIN 4X1 + 3X2
Subject to constraints (1) 2X1 + X2 > 12
(2) X1 – X2 < -3
Suppose the first constraint were changed to:
(1) 2X1 + X2 > 8
Use the graphical method to determine if the product mix would be
the same.
(3)For this linear programming problem, do algebraic sensitivity
range. For what range of values of the objective function
coefficient c1 does the optimum stay at the current corner point?
MAX c1x1 + c2x2 = 5x1 + 12x2
subject to constraints
(1)
2x1 +
x2 < 200
(2)
x1 + 2x2 < 300
4) Linear Programming Formulation
FORMULATE the following as linear programming model: You want to maximize
the number of votes for your candidate by scheduling campaign workers to phone
voters to remind them to vote and by giving a ride to the polling place. You
have 12 worker-hours available in the morning, and 14 worker-hours available
in the afternoon. Each morning phone call requires one minute, and each
afternoon phone call requires two minutes. Each morning ride requires 20
minutes, and each afternoon ride requires 30 minutes. You have enough gas in
the tank to make at most 100 rides. Each morning phone call will obtain one
vote, while each afternoon phone call will obtain two votes. Each morning
ride will obtain three votes, and each afternoon ride will obtain four votes.
(a) Decision variables:
(b) Write objective function in mathematical form:
(c)Write
constraints in mathematical form (do NOT try to solve!):
(5) FORMULATE as linear programming, but do NOT try to solve: How many
servings of each food should you eat to minimize total cost, subject to
constraints: at least 1000 calories but no more than 1800 calories; at least
15 grams of fat but no more than 40 grams of fat; at least 25 grams of
protein; no more than 19 milligrams of cholesterol. You are given:
food
calories
cholesterol cost
fat
protein
fish
400
100
3
4
90
beef
700
300
4
80
100
lettuce
40
0
2
0
2
beans
500
0
1
2
20
(a) Define DECISION variables (omit slack)
(b) Write objective function in mathematical form
(c) Write constraints in math form (omit slack; do NOT try to solve!):
(6) FORMULATE as linear programming, but do NOT try to solve: How many tv and
radio commercials should you buy to minimize total cost, given that each tv
commercial costs
$ 100,000 and reaches 1,000,000 customers, of whom 60% are male;
each radio commercial costs $ 50,000 and reaches 400,000 customers, of whom
70% are female. Use at least twice as many radio commercials as tv
commercials; reach at least 3,000,000 customers; at least 40% of the audience
is male; available space limits tv commercials to 5.
(a) Define DECISION variables (omit slack)
(b) Write objective function in mathematical form
(c) Write constraints in math form
ck fig for first 3 problems only
(1) Make 45 units of Alaska and 5 units Arabian at $125 cost
(2) orig solution: (3,6)
new solution:(1.7,4.7)
output insensitive
(3) C1 < 6