Class Exercise On Linear Programming PDF
Class Exercise On Linear Programming PDF
Class Exercise On Linear Programming PDF
PROBLEM 1
Reddy Mikks produces both interior and exterior paints from two raw materials, M1 and M2. The following table
provides the bas+ic data of the problem:
Raw Material, M1
Raw Material, M2
Profit per ton ($1000)
Maximum daily
availability (tons)
24
6
A market survey indicates that the daily demand for interior paint cannot exceed that of exterior paint by more than
1 ton. Also, the maximu m daily demand of interior paint is 2 tons.
Reddy Mikks wants to determine the optimum (best) product mix of interior and exterior paints that maximizes the
total daily profit.
PROBLEM 2
A furniture company produces a variety of products. One department specializes in wood tables, chairs, and bookcases.
These are made using three resources: labor, wood, and machine time. The department has 60 hours of labor available
each day, 16 hours of machine time, and 400 board feet of wood. A consultant has developed a linear programmin g
model for the department:
1
Quantity of tables
Quantity of chairs
Quantity of bookcases
Maximize
401 + 30 2 + 45 3
(Profit)
Subject to
Labor
21 + 1 2 + 2.5 3 60
hours
Machine
.8 1 + .6 2 + 1.0 3 16
hours
Wood
301 + 20 2 + 30 3 400
board-feet
1 10
Tables
board-feet
1 , 2 , 3 0
Answer these questions posed by department manager Barbara Brady:
(a)
(b)
(c)
(d)
(e)
(f)
PROBLEM 3
A manager of an automobile dealership must decide how many cars to order for the end of the model year. Midsize
cars yield an average profit of $500 each, and compact cars yield an average of $400 each. Either type of car will
cost the dealership $8,000 each and no more than $720,000 can be invested. The manager wants at least 10 of each
type of car but no more than 50 midsized cars and no more than 60 of the compact cars.
a) Formulate the linear programming model of this problem.
b) Solve for the optimal quantities of each type of car and the optimal value of the objective func tion.
PROBLEM 4
A wood products firm uses leftover time at the end of each week to make goods for stock. Currently, there are two
products on the list of items that are produced for stock: a chopping board and a knife holder. Both items require
three operations: cutting, gluing, and finishing. The manager of the firm has collected the following data on these
products:
Item
Chopping board
Knife Holder
Profit
per Unit
$2
$6
Times
Cutting
1.4
0.8
The manager has also determined that during each week 56 minutes are available for cutting, 650 minutes are
available for gluing, and 360 minutes are available for finishing. The manager wants to know the number of
chopping board and knife holder to be manufactured so that his total profit is maximized.
a) Formulate this problem as a linear programming model.
b) Determine the optimal quantities of the decision variables.
c) Which resources are not completely used by your solution? How much of each resources is unused?
PROBLEM 5
The manager of an inspection department has been asked to help reduce a backlog of safety devices that must be
inspected. There are two types of safety devices: one for construction workers and one for window washers. The
manager will be permitted to select any combination of items because new testing equipment will soon be asked to
help generate revenue. The revenue for each construction device is $60, and the revenue for each window-washing
device is $40. The manager has obtained data on necessary inspection operations, which are
Operation
Test #1
Test #2
Test #3
Time per
Construction
3/4
1/4
1/2
Unit (minutes)
Window Washing
1/3
1/2
1/4
Total Time
Available (minutes)
75
50
40
PROBLEM 6
A pharmaceutical company is investigating the possibility of marketing a new dietary supplement that would contain
iron, calcium, and phosphorous. The supplement would be made by mixing together three inputs, which the company
refers to as T5, N1, and T4. The amounts of the three minerals (mg per ounce) contained in each input, the min imu m
and maximu m levels of each mineral per 12-ounce bottle, and the cost per ounce of the inputs are shown in the
following Table.
Cost per Ounce
Input
Mineral
$0.75
T5
$0.60
N1
$0.55
T4
Minimum per
Bottle
Maximum
per Bottle
Iron
Calcium
Phosphorous
10
400
800
16
600
550
12
800
500
100mg
6,000mg
6,600mg
150mg
8,000mg
8,000mg
The manager would like to know what the lowest cost combination of inputs is that would achieve the
desired dietary ranges for the three minerals on a per-bottle basis. Formulate this problem as an LP model.
PROBLEM 7