Introduction to Supply Chain Management Homework 1 (25 points)For all the problems, to receive full scores, you have to show your complete and accurate work. If you only provide the final answers without showing your computations, you will not be assigned a full score (or you will miss the opportunity of receiving partial credit). All homework is to be turned in on time through D2L.Problem 1: Line Balancing (13 points) First shift employees at Toyota work from 6am to 2pm Monday through Friday. Everyone on the assembly line is allowed a 30 minute lunch and two 20 minute breaks. Other cross-trained associates cover lunches and breaks for the associates on the assembly line so the line doesnt stop. After three weeks at Toyota, you record the processes of the assembly line are laid out in the following manner: Task Predecessor Average Time (sec) A none 100 B none 150 C A 93 D B 120 E B 86 F C 84 G D, E 65 H F, G 15The Plant Manager needs first shift to achieve an output of 100 units per shift. Compute the Takt time for the line (2 points). What is the theoretical minimum number of workstations? (2 points) Draw the precedence diagram (2 points). Assign tasks to work stations and you must use the largest eligible task heuristic rule to break any ties. Show which tasks are assigned to each workstation (3 points). Compute the efficiency and percent idle time for the system (2 points). What is the maximum output that could be achieved by a single assembly line in 8 hours? (2 points)Problem 2: Forecasting (6 points) Jun Jul Aug Sept Oct Nov Dec Units Sold 255 305 298 268 321 359 319Given these sales figures over the last 7 months, your boss needs you to create a forecast model that can be used to forecast sales in the future. Use three different forecasting methods (last period, 2 period moving average and 3 period moving average) to determine which forecasting method would be best to forecast future sales. For your measure of best, recommend the company use the method with the lowest mean absolute deviation (MAD). Calculate the MAD for each of the 3 forecasts (4 points). After you have selected the best forecasting method, what would you tell your boss is the forecasted sales for January? (2 points).Problem 3: Forecast Accuracy (6 points) Your company released a new product in December last year. Prior to December, the Marketing Department provided their forecasted sales. The product has been on the market for 5 weeks now and the table below shows the actual sales and Marketings forecast of units sold. Week Actual Sales (units) Forecasted Sales (units) 1 3,221 4,000 2 4,788 4,500 3 5,372 5,200 4 6,051 5,900 5 6,716 6,200Calculate the MFE for the forecast (3 points). Calculate the MAPE for the forecast (3 points).