What is linear programming? Briefly explain the usefulness of the model.

Purchasing and Supply Chain Management
6th Edition
ISBN:9781285869681
Author:Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson
Publisher:Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson
ChapterC: Cases
Section: Chapter Questions
Problem 5.1SC: Scenario 3 Ben Gibson, the purchasing manager at Coastal Products, was reviewing purchasing...
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A seminar was recently attended by the Managing Director of XYZ Manufacturing Company Limited located at Sheffield. The focus of the seminar was “optimising scarce resources utility in a manufacturing setting with particular reference to linear programming”. On his return to his base, he called for a meeting with the Management to share his experience from the seminar and the impact this will have on the decision by the Board to produce two major products in the years ahead.

A group of external research experts had previously been commissioned and the following represents information from the research carried out by them

The expected products are “Best” and “Smart” with expected costs statistics as follows:

 

Best

£

Smart

£

Material costs

(5kg@£50/kg)

250

(3kg@£50/kg)

150

Labour costs

       

Machinery time

(4 hours @£15/Hr)

60

(2hours @£15/Hr)

30

Other Processing Time

(4 hours @£10/hr)

40

(5hours@£10/Hr)

50

The applicable pricing policy is based on total cost of production plus 20% mark up on cost.

The Company’s overhead is expected to be £10,000,000 with normal production of 200,000 units of Best and 100,000 units of Smart and overhead absorbed on the basis of 3 to 2 respectively.
The resources below will be available to the company in the following year.

  1. Materials 1,800,000kgs

  2. Machine time 800,000 hours

  3. Other process time 1,400,000

Required:

  1. What is linear programming? Briefly explain the usefulness of the model.

  2. Compute the prices that will be adopted by the company for the two products using the company policy.

  3. Advise the company on the output that needs to be produced to maximise its total profit, supporting your answer with full financial analysis. 

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