BS 341 EXAM TUTORIAL
LESA PANTANSHI
2ND MAY, 2024
PRINCE DANIELS – 2024
QUESTION ONE
A company manufactures three types of leather belts, namely A, B
and C. The material cost for making type A is K60; B is K52 & C is
K96 per unit respectively. Labour costs are K44/unit on type A,
K36/unit on type B and K70/unit type C. In order to distribute the
belts to various parts of the country, the distribution costs are set at
6% prime cost on each product type per unit. The selling prices per
unit for the products are K150.24, K123.28 and K195.96
correspondingly. To manufacture the belts, type A requires 2 parts
of leather, 2 parts of fancy buckle and 4hrs machining time. Type B
requires 5 parts of leather and fancy buckle each, and 2hrs of
machining. Type C requires 10 parts of leather, 3 parts of fancy
buckle and 2hrs of machining time. A maximum of 900 leather parts
are available per day, with 400 fancy buckles available as well as
600hrs machining time available to produce all the belt types.
i)
Formulate the problem and using the simplex algorithm,
determine how many belts of each type should be produced to
maximize the total profit
ii)
Determine the ranges of optimality for the objective function
coefficients of all the belt types
QUESTION TWO
A Zambian company producing dairy products has two plants
located at Lusaka and Kitwe with a capacity of 200 hectoliters and
100 hectoliters per week respectively. The company supplies the
dairy products to its four outlets situated in Ndola, Chongwe,
PRINCE DANIELS – 2024
Mazabuka and Mongu which have a maximum demand of 75, 100,
100 and 30 hectoliters respectively.
The transportation costs in kwacha differs which is shown in the
table below
Ndola
Chongwe
Mazabuka
Mongu
Lusaka Plant
K90
K90
K100
K110
Kitwe Plant
K50
K70
K130
K85
a) Write a linear programming (mathematical model) for this
problem
b) Using appropriate methods solve this minimization problem and
determine the optimal solution
c) Write the linear solutions for this problem
QUESTION THREE
a) Given the following final simplex tableau where the coefficients in the initial tableau
were - 2 for X1 and - 3 for X2.
Basic
?
?
?
Z
X1
1
0
0
?
X2
0
1
0
?
S1
0
0
1
?
S2
1
-2
1
?
S3
1
-1
1
?
RHS
250
100
125
?
i) Fill in the missing values of the final tableau
ii) Is this problem a maximization or a minimization problem? How can you tell?
iii)
If the original RHS value for the 3rd constraint was 600, determine the range for the
RHS value of the 3rd
PRINCE DANIELS – 2024
QUESTION FOUR
b) Debonair Pizza at Mukuba Mall makes two types of Pizza, the Cram-Decker and the
Triple Decker. The only scarce resource that is needed to produce Pizza is labour. At
present, the company has two shifts. In shift one a worker should be willing to work up
to 60 hours per week and is paid K25 per hour. In shift two, a worker will work up to
40 hours per week for K30 per hour. The price as well as the resources required to
make each type of Pizza are given on Table below:
Cram-Decker
Price K300
i.
Triple Decker
Resource;
Price K270
Resource;
Shift One 4 hour labour
Shift One 6 hours labour
Shift Two 4 hour labour
Shift Two 2 hours labour
Raw material cost K50
Raw material cost K40
Formulate an LP for this problem and solve the problem using the simplex method.
How many Cram-Decker and Triple Decker should Debonair Pizza produce to
maximize profits?
ii.
For what values of the price of a Cram-Decker would the current basis remain
optimal?
QUESTION FIVE
The output from excel solver is shown below
PRINCE DANIELS – 2024
a) What production plan should be implemented in order to
maximize the contribution of the firm's profit from this product
division?
b) Suppose the standard work hours for an employee in labour, and
processing departments is 340hrs per month. How many employees
should go on VSP in these departments and what would be the
impact on the production output?
c) The Director of operations is of the view that they decrease the
quantity of white spoon sugar produced by decreasing about
14500kgs of material. If they went ahead with this decision, what
quantity white spoon sugar should now be produced?
d) The Marketing Manager also thinks increasing the contract
quantity supplied to Shoprite from the current 3000kgs to 7000kgs
will improve the company’s viability. Should they do so? How will this
decision impact on the company’s profitability?
e) It is also observed that Logistics costs account for a significant
portion of a company’s costs. The Procurement Manager is therefore
tasked to find means of reducing costs in the supply chain by
optimizing the activities associated with supply chain and logistics.
One area which comes into the Manager’s mind is to renegotiate the
supply contracts of raw materials supplied by Mazabuka sugarcane
farmers. What should be his negotiation bargain?
PRINCE DANIELS – 2024
f) Suppose Zimbabwe’s white sugarcane farmers offered to supply
raw materials to Zambia sugar at K6/kg. Should Zambia sugar
accept this offer? Explain
g) Suppose that the company could deliver 1000kgs less than the
contracted amount of Sugar to Shoprite by paying a penalty of K6/kg
shortage. Should they do so?
h) If the VSP doesn’t work according to plan, Zambia Sugar will be
forced to shut most of its operations. Suggest any three departments
layoffs should begin from and why?
PRINCE DANIELS – 2024