Part C: Cost of procuring boilers
This part of the coursework requires you to use linear programming techniques to determine the best way to minimise the cost of supplying boilers to Lamberts Heating
As well as manufacturing radiators (as mentioned in Part A), Lamberts Heating is also reviewing the way it procures boilers to enable the installation of domestic heating systems.
The purchasing department has identified three possible suppliers of boilers; Apex, Brunswich and Centrale. It has also identified five kinds of domestic boiler that it wants to purchase so it can supply and fit these boilers to a variety of sizes of homes.
The five boilers are known and coded by Italian numbers as most are manufactured in Italy ; Uno (1), Duo (2), Tre (3), Quattro (4) and Cinque (5).
The table below gives the cost of each boiler (in £s) from each supplier. The final row of the table specifies the minimum requirement of each type of boiler per year. Please note that not all boilers are available from each supplier.

Uno
Duo
Tre
Quattro
Cinque
Apex
500
750
300
—
450
Brunswich
—
725
320
875
420
Centrale
480
775
310
900
—
Requirement
(number of boilers)

2000

1500

3000

2500

2200

There are certain limitations that have to be taken into account;
· Apex can supply no more than 1,000 of the Tre boiler each year.
· Brunswich can supply no more than 800 of the Duo boiler each year.
· Centrale can supply no more than 1,800 Uno boilers each year.
Lamberts Heating wants to meet its requirement for the number of boilers needed each year at the minimum cost.
Task
You are expected to use MS Excel software for this task. However, we will accept printouts from any other Linear Programming software.
Appendix
· Define the meaning of any decision variables you are using.
· Formulate the situation described above as a linear programming problem.
· Include your computer input of the problem (and show any formulae used)
· Include the “Answer Report” and “Sensitivity Report” printouts
Report
Write a brief report to the management of Lambert Heating detailing the cheapest way of meeting their need for boilers.
This report, written in a formal style of English, should include:
· The nature of the problem being solved
· The suggested purchasing plan
· The cost of the suggested purchasing plan.
· The robustness of the plan. Provide details of the ranges of costs of boilers from each suggested supplier for which your suggested plan remains optimal, and advise the company when they will have to generate a new plan. Do not just provide lists but consider your answers in the context of the question.
· At present, Apex can supply no more than 1,000 of the Tre boiler each year. If this limit was changed so that Apex could now supply 1,100 Tre boilers, explain what effect this would have on the total minimum cost?
A successful assignment (for Part C of this assignment) should include:
§ Well-defined decision variables and a correct formulation of the problem.
§ Appropriate use of Excel (or other software) to produce a solution to the problem.
§ Producing a well-written, well-structured report that enables management to understand how to procure boilers at the minimum price. This report should include details of your suggested purchasing plan and the cost of this plan.
§ The advice to management should also enable them to determine the range of prices for each boiler for which your purchasing plan is valid.
§ The implications of the increased capacity to supply by Apex should be clearly described.

Note: The above is illustrative, covering only the main points of the assignment.
Suggested length: 500 words
This part of the assignment (Part C) represents 30% of your marks on this piece of coursework.