Tutorial 10

BQA1014 Quantitative Analysis Models for Business (Tutorial 10)
Tutorial 10
1. Abang Adik Sdn. Bhd. produces two types of product, X and Y. These products used
two types of raw materials. Product X requires 1 pound of material A and 2 pounds of
material B. Product Y requires 2 pounds of material A and 1 pound of material B. The
total availability of the two materials is 40 pounds of material A and 50 pounds of
material B. Due to the production constraints, at most 15 units of product Y produced
each day. The profit contribution per unit of product X is RM30 and product Y is
RM20.
(a) Formulate the above information into the Linear Programming model.
(b) Graph the above problem and show the feasible region clearly.
(c) Find the optimal solution and the maximum profit of Abang Adik Sdn Bhd.
(d) If the profit of the product X is RM20 and the product Y is RM30, will the
optimum solution be affected? What will be the new maximum profit?
2. I- Home Corporation manufactures two products, benches and tables. The company has
two main resources, carpenters and a supply of redwood for use in furniture. In a
month, there are 1200 hours of labour and 8,000 feet of redwood available. Each bench
requires 2 labour hours and 10 feet of redwood while each table requires 3 labour hours
and 25 feet of redwood. Completed benches will yield a profit of RM15 each and tables
will result in a profit of RM18 each. One of its customers has ordered 50 benches and
100 tables. The company’s aim is to obtain maximum profit while meeting customer’s
order.
(a) Formulate the above problem into a Linear Programming problem.

(b) Graph and show the feasible region of the above problem clearly.
(c) Advise I-Home on the optimal solution and the associated maximum profit by
using the method of corner.
(d) What would be the effect on the optimal solution if the profit gained per bench
has been increased to RM18 and profit gained per table has been reduced to
RM16?
Page 1|
3. An appliances manufacturer produces two types of slow cooker: Type 1 and Type 2.
Both models require fabrication and assembly work; each Type 1 slow cooker requires
4 hours of fabrication and 2 hours of assembly, and each Type 2 slow cooker requires 2
hours of fabrication and 6 hours of assembly. There are 700 hours of fabrication and
800 hours of assembly time available this month. Each Type 1 slow cooker contributes
RM50 to profit, and each Type 2 contributes RM60 to profit. The manufacturer
received orders of at least 80 units of Type 1 slow cooker and a minimum of 70 units of
Type 2 slow cooker. Because of the company policy, the number of units of Type 2
slow cooker produced must be less than or equal to the number of units of Type 1 slow
cooker.
a. Formulate a liner programing model of this problem.

b. Graph and show the feasible region of the above problem clearly.
c. How many units of each type of slow cooker should the company produce in order
to maximise the profit? What is the maximum profit?
4. A factory manufactures two products which are Product X and Product Y. Each of
which must pass through two production processes at machine A and machine B.
Product X requires 5 hours at machine A and 4 hours at machine B, while product Y
requires 5 hours at machine A and 2 hours at machine B. The maximum capacity of
machine A for a certain period is 6000 hours and, due to cost and manpower agreement,
machine B must be used for at least 3600 hours over the same period. Due to
sales agreement, at least 700 units of Product X must be produced, while a maximum of
600 units of Product Y will be produced over the given period. Product X has a profit
of RM10 and Product Y has a profit of RM14.
(a) Formulate the above problem as a Linear Programming problem.

(b) Graph and show the feasible region of the above problem clearly.
(c) Find the optimal solution and the associated maximum total profit.
Page 2|
5. A company has developed two newly products namely Product A and Product B. A
new plant has also been built to produce these two products. It is known that this new
plant can be operated for 96 hours per week. A unit of Product A will require 4 hours of
production and a unit of Product B will require 6 hours of production. It is estimated
that Product A will make a profit of RM80 and Product B of RM100 for each unit sold.
The marketing research department has found that only maximum of 15 units of
Product A and 12 units of Product can be sold each week and production will not be
more that estimated demand.
(a) Formulate the above problem as a Linear Programming problem.

(b) Graph the above Linear Programming problem into a suitable diagram and shade
the feasible region clearly.
(c) Find the optimal solution and the maximum total profit.
(d) What would be the effect on the optimal solution if the profit of the Product A
change to RM90?
6. Cergas Claims Sdn. Bhd. processes insurance claims for large national insurance
companies. Most of the claim processing is done by a large pool of computer operators,
some of whom are permanent and some of whom are temporary. A permanent operator
can process 15 claims per day, whereas a temporary operator can process 10 claims per
day, and on average the company processes at least 465 claims each day. The company
has 40 computer workstations. A permanent operator generates about 0.6 claims with
errors each day, whereas a temporary operator averages about 1.2 defective claims per
day. The company wants to limit claims with errors to 27 per day. A permanent
operator is paid RM65 per day, and a temporary operator is paid RM45 per day. The
company wants to determine the number of permanent and temporary operators to
hire in order to minimize costs.
(a) Formulate a linear programming model for this problem.
(b) Solve this model by using graphical analysis and show the feasible region.
(c) How many permanent and temporary operators should be hired so that the cost
will be minimized? What is the minimum cost?
Page 3|
Page 4|

Tutorial 10

Uploaded by

Copyright:

Available Formats

Tutorial 10

Uploaded by

Document Information

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Tutorial 10

Uploaded by

Copyright:

Available Formats

BQA1014 Quantitative Analysis Models for Business (Tutorial 10)

(a) Formulate the above problem into a Linear Programming problem.

a. Formulate a liner programing model of this problem.

(a) Formulate the above problem as a Linear Programming problem.

(a) Formulate the above problem as a Linear Programming problem.

You might also like