Question 1 Mark: 2+ 5+4+ 4 = 15 A small firm intends to increase the capacity of a bottleneck operation for producing a product by adding a new machine. Two alternatives, A and B, have been identified and the associated costs and revenues have been estimated. Annual fixed costs would be $30000 for A and $25,000 for B; variable costs per unit would be $10 for A and $12 for B; and the revenue per unit would be $25. i. ii. iii. iv. Find the total cost functions for alternatives A and B, and the revenue function Draw both the total cost functions and the revenue function in the same figure. Find the break-even point for the alternatives A and B and show it in the figure Is there any volume of output at which both the alternatives yield the same profit? If so, show it in the figure. If not, identify the volume of output at which the alternatives are indifferent. Question 2 Mark: 4+ 2+2+ 5+2 = 15 a) In order to complete the wing assembly for an experimental aircraft, a company has laid out the major steps and seven tasks involved. These tasks have been labeled A through G in the following table, which also shows their estimated completion times in minutes and immediate predecessors. Task Immediate Predecessors ---- A B A Task time (in minute) 0.60 0.55 0.80 0.70 1.00 0.80 0.50 D E F G B, D B, E F i) Draw the precedence diagram. ii) Assuming an 8-hour shift, compute the cycle time needed to obtain an output of 400 units per shift. iii) Determine the minimum number of workstations required. iv) Assign tasks to the required number of workstations and show the assignment of tasks in a diagram. v) Find the percentage of idle time and the efficiency of the capacity utilization