QUESTION 2 A construction company distributes its products by trucks loaded at its loading station. A backacter in conjunction with trucks are used for this purpose. If it was found out that on an average of 12 trucks per hour arrived and the average loading time was 3 minutes for each truck. A truck must queue until it is loaded. The backacter's daily all-in rate is GH 1000 and that of the truck is GH 400. a) Compute the operating characteristics: L, L, W, W., and P. b) The company is considering replacing the backacter with a bigger one which will have an average service rate of 1.5 minutes to serve trucks waiting to have their schedules improved. As a manager, would you recommend the new backacter if the daily all-in rate is GH 1300. c) The site management is considering whether to deploy an extra backwater to assist the existing one. The daily all-in-rate and efficiency of the new backwater is assumed to be the same as that of the existing backwater. Should the additional backwater be deployed? QUESTION 3 A university cafeteria line in the student center is a self-serve facility in which students select food items they want and then form a single line to pay the cashier. Students arrive at a rate of about four per minute according to a Poisson distribution. The single cashier ringing up sales takes about 12 seconds per customer, following an exponential distribution. a) What is the probability that there are more than two (2) students in the system? b) What is the probability that the system is empty? c) How long will the average student have to wait before reaching the cashier? d) What is the expected number of students in the system? e) What is the average number in the system? f) If a second cashier is added (who works at the same pace), how will the operating characteristics have computed in parts b), c), d) and e) change? Assume that customers wait in a single line and go the first available cashier. QUESTION 4 Stivo company limited manufactures two types of steel beams. The beams consume a maximum of 15 litres of Substance A and another 15 litres of Substance B. In the market there are only two classes of Chemicals: Type X, with a composition of one unit of A to five units of B, and another type, Y, with a composition of five units of A to one of B. The price of Type X is GHS10 and Type Y, GHS30. What are the quantities of each type of chemical that have to be purchased to cover the manufacturing of the beams at a maximum cost? a) Formulate the problem of the quantity of each chemical to purchase as a linear program. b) Solve this linear program graphically. QUESTION 5 a) Sarobi construction company limited is a Cape Coast based construction company. The company has been awarded a GHS700,000.00 contract by The Cape Coast Polytechnic. The contract involves the construction of ten (10) 3-bedroom housing unit for the senior members of the polytechnic. The breakdown of the five operations that occur in the construction sequence, duration and the number of gangs are shown in table 1. As a project manager of the company, you have been asked by the board of directors of Sarobi to prepare and present a line of balance programme at a board meeting. You are to prepare the following for the presentation: i. Sequence logic for the operation. ii. Line of balance diagram showing all the calculations and steps involved. iii. Allow a minimum buffer of 1 week between one operation and next. b) State the reason for the introduction of buffers at the start or finish of an operation in the line of balance diagram plotting. Table 1 Operation Duration No. of Gangs Site preparation and foundation 2 External wall 3 Roof construction Internal finishes External works 2 4 1 4 QUESTION 2 A construction company distributes its products by trucks loaded at its loading station. A backacter in conjunction with trucks are used for this purpose. If it was found out that on an average of 12 trucks per hour arrived and the average loading time was 3 minutes for each truck. A truck must queue until it is loaded. The backacter's daily all-in rate is GH 1000 and that of the truck is GH 400. a) Compute the operating characteristics: L, L, W, W., and P. b) The company is considering replacing the backacter with a bigger one which will have an average service rate of 1.5 minutes to serve trucks waiting to have their schedules improved. As a manager, would you recommend the new backacter if the daily all-in rate is GH 1300. c) The site management is considering whether to deploy an extra backwater to assist the existing one. The daily all-in-rate and efficiency of the new backwater is assumed to be the same as that of the existing backwater. Should the additional backwater be deployed? QUESTION 3 A university cafeteria line in the student center is a self-serve facility in which students select food items they want and then form a single line to pay the cashier. Students arrive at a rate of about four per minute according to a Poisson distribution. The single cashier ringing up sales takes about 12 seconds per customer, following an exponential distribution. a) What is the probability that there are more than two (2) students in the system? b) What is the probability that the system is empty? c) How long will the average student have to wait before reaching the cashier? d) What is the expected number of students in the system? e) What is the average number in the system? f) If a second cashier is added (who works at the same pace), how will the operating characteristics have computed in parts b), c), d) and e) change? Assume that customers wait in a single line and go the first available cashier. QUESTION 4 Stivo company limited manufactures two types of steel beams. The beams consume a maximum of 15 litres of Substance A and another 15 litres of Substance B. In the market there are only two classes of Chemicals: Type X, with a composition of one unit of A to five units of B, and another type, Y, with a composition of five units of A to one of B. The price of Type X is GHS10 and Type Y, GHS30. What are the quantities of each type of chemical that have to be purchased to cover the manufacturing of the beams at a maximum cost? a) Formulate the problem of the quantity of each chemical to purchase as a linear program. b) Solve this linear program graphically. QUESTION 5 a) Sarobi construction company limited is a Cape Coast based construction company. The company has been awarded a GHS700,000.00 contract by The Cape Coast Polytechnic. The contract involves the construction of ten (10) 3-bedroom housing unit for the senior members of the polytechnic. The breakdown of the five operations that occur in the construction sequence, duration and the number of gangs are shown in table 1. As a project manager of the company, you have been asked by the board of directors of Sarobi to prepare and present a line of balance programme at a board meeting. You are to prepare the following for the presentation: i. Sequence logic for the operation. ii. Line of balance diagram showing all the calculations and steps involved. iii. Allow a minimum buffer of 1 week between one operation and next. b) State the reason for the introduction of buffers at the start or finish of an operation in the line of balance diagram plotting. Table 1 Operation Duration No. of Gangs Site preparation and foundation 2 External wall 3 Roof construction Internal finishes External works 2 4 1 4
