A company undertakes both construction of new houses and also the repair and renovation of old building. Due to the competition in the market, it has become necessary for the companys long term plans to obtain a suitable mix of new houses and repair work each year. For planning purpose, the profit on new houses is taken to be 20% of their total value whereas on repair and renovation is 25%.

To avoid the problem of having to acquire large amount of land for the building of new houses, the company always plan for at least 4,000,000 of repair and renovation work each year but at the same time the company ensures that repairs and renovation do not account for more than half of their total work load. Furthermore, in costing all new and repair work, 5% of the total value of the work load is included to cover the companys actual fixed overheads which have been estimated at 500,000 for the coming year.

The other major consideration is the amount of skilled labour which is available. It has been estimated that 1,000,000 of new house building involves 12-man years of skilled labour, whereas 1,000,000 of repair and renovation work requires 18-man years of skilled labour. The company currently employs 180 skilled workmen and it would be difficult to recruit more skilled labour in the short term.

Required

(a) Develop a linear programming model of the planning problem facing the company. (8marks)

(b) Using the graphical approach, determine the total value of both new building work and repair and renovation work that should be undertaken next year to maximize profit. (12 marks)

(c) What increase in profit (if any) would be achieved if the company were to remove the condition of having at least 4,000,000 of repair and renovation work each year? (10marks)

NOTE: Please Plot the graph on a graph sheet, scan it and attached it to the document.