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: (5kg@50/kg) 250 Best Material costs Labour costs Machinery time (4 hours @15/Hr) 60 Other Processing Time (4 hours @10/hr) 40 Smart (3kg@50/kg) (2hours @15/Hr) (5hours@10/Hr) 150 30 50 The applicable pricing policy is based on total cost of production plus 20% mark up on cost. The resources below will be available to the company in the following year. i. Materials 1,800,000kgs ii. Machine time 800,000 hours iii. Other process time 1,400,000 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. Required: a. What is linear programming? Briefly explain the usefulness of the model. (5 Marks) b. Compute the prices that will be adopted by the company for the two products using the company policy. (5 Marks) c. Advise the company on the output that needs to be produced to maximise its total profit, supporting your answer with full financial analysis. (10 Marks) d. i. Explain the meaning of "shadow prices" and comment on the usefulness of it and its limitation. ii. Calculate the shadow prices of the constraints. (5 Marks) (7 Marks) e Assuming the company's position in (c) is maintained for three years with an investment cost of 45,000,000 on the day of commencement of manufacturing business, using a cost of capital of 15%. i. Can this venture be justified for the period? ii. What is the breakdown discount factor for this project? (4 Marks) (4 Marks) (Total 40 Marks)