The board of UCSI Construction Sdn. Bhd. is considering the company’s plan for...
...the next financial year. UCSI C? The board of UCSI Construction Sdn. Bhd. is considering the company’s plan for the next financial year. UCSI Construction Sdn. Bhd. undertakes both the construction of new houses and also the repair and renovation of old buildings, and it is important for the company’s long term plans to obtain a suitable mix of new houses and repair work each year. For planning purposes, the profit on new houses is taken to be 25% of their total value whereas on repairs and renovations it is 30%.
To avoid the problems of having to acquire large amounts of land for the building of new houses, UCSI Construction Sdn. Bhd. always plans for at least RM10 millions of repairs and renovations each year but at the same time the company ensures that repairs and renovations do not account for more than half of their total workload. Furthermore, in costing all new and repair work, 3% of the total value of the work is included to cover fixed overheads. It is the board’s wish that the total of these overhead charges does in fact cover the company’s actual fixed overheads which have been estimated at RM0.9 million for the coming year.
The other major consideration is the amount of skilled labour (bricklaying, plastering, plumbing, carpentry and electrical work) which is available. It has been estimated that RM1 million of new house building involves 18 man years of skilled labour, whereas RM1 million of repair and renovation work requires 12 man years of skilled labour. The company currently employs 900 skilled workmen and it would be difficult to recruit more skilled labour in the short term.
As a business entity, UCSI Construction Sdn. Bhd. wants to maximize profit.
a)Develop a linear programming model of the planning problem facing UCSI Construction Sdn. Bhd. by using Corners Method with graph.
Show clearly:
(i)The decision variables
(ii)The objective function
(iii)All the constraints
(iv)The feasibility region with corners
(v)The solution with workings
(15 marks)
b)Develop a linear programming model of the planning problem facing UCSI Construction Sdn. Bhd. by using Simplex Method:
(i)Reformulate the linear program in an equation form that is suitable for the simplex method.
(ii)Show the initial simplex tableau, with appropriate headings/labels.
(iii)Apply the simplex method to determine the optimum value of the decision variables and the objective function. Show all the iterations in simplex tableaus. Write down the final solutions.
...the next financial year. UCSI C? The board of UCSI Construction Sdn. Bhd. is considering the company’s plan for the next financial year. UCSI Construction Sdn. Bhd. undertakes both the construction of new houses and also the repair and renovation of old buildings, and it is important for the company’s long term plans to obtain a suitable mix of new houses and repair work each year. For planning purposes, the profit on new houses is taken to be 25% of their total value whereas on repairs and renovations it is 30%.
To avoid the problems of having to acquire large amounts of land for the building of new houses, UCSI Construction Sdn. Bhd. always plans for at least RM10 millions of repairs and renovations each year but at the same time the company ensures that repairs and renovations do not account for more than half of their total workload. Furthermore, in costing all new and repair work, 3% of the total value of the work is included to cover fixed overheads. It is the board’s wish that the total of these overhead charges does in fact cover the company’s actual fixed overheads which have been estimated at RM0.9 million for the coming year.
The other major consideration is the amount of skilled labour (bricklaying, plastering, plumbing, carpentry and electrical work) which is available. It has been estimated that RM1 million of new house building involves 18 man years of skilled labour, whereas RM1 million of repair and renovation work requires 12 man years of skilled labour. The company currently employs 900 skilled workmen and it would be difficult to recruit more skilled labour in the short term.
As a business entity, UCSI Construction Sdn. Bhd. wants to maximize profit.
a)Develop a linear programming model of the planning problem facing UCSI Construction Sdn. Bhd. by using Corners Method with graph.
Show clearly:
(i)The decision variables
(ii)The objective function
(iii)All the constraints
(iv)The feasibility region with corners
(v)The solution with workings
(15 marks)
b)Develop a linear programming model of the planning problem facing UCSI Construction Sdn. Bhd. by using Simplex Method:
(i)Reformulate the linear program in an equation form that is suitable for the simplex method.
(ii)Show the initial simplex tableau, with appropriate headings/labels.
(iii)Apply the simplex method to determine the optimum value of the decision variables and the objective function. Show all the iterations in simplex tableaus. Write down the final solutions.