Answer the following question by indicating either True or False 1) The break-even quantity is the volume at which the total revenue equals total cost. 2) The variable cost is the portion of total cost that remains constant regardless of changes in levels of production. 3) Fixed cost is the portion of the total cost that remains constant regardless of changes in levels of output. 4) Sensitivity analysis is a technique for systematically changing parameters in a model to determine the effects of such changes. 5) A preference matrix is a table that allows the manager to rate an alternative according to one performance criterion. 6) Operations management refers to the direction and control of inputs that transform processes into products and services. 7. As a functional area of a business, Operations translates materials and services into outputs. 8. A critical path is any sequence of activities between a project's start and finish. 9. The earliest start time is never the same as the latest start time. 10. To obtain the latest start and latest finish time, we must work forward through the network. Question two [20 marks] Consider the following data for a project. a) Draw the network diagram for this project b) Determine the critical path and project duration c) Calculate the slack for each activity Question three [20 marks] Metal Discovery Group (MDG) is a company set up to conduct geological explorations of parcels of land in order to ascertain whether significant metal deposits (worthy of further commercial exploitation) are present or not. Current MDG has an option to purchase outright a parcel of land for Rand 3m. If MDG purchases this parcel of land then it will conduct a geological exploration of the land. Past experience indicates that for the type of parcel of land under consideration geological explorations cost approximately Randim and yield significant metal deposits as follows: - manganese 1% chance - gold 0.05% chance - silver 0.2% chance Only one of these three metals is ever found (f at all), Le. there is no chance of finding two or more of these metals and no chance of finding any other metal. If manganese is found then the parcel of land can be sold for Rand 30m, if gold is found then the parcel of land can be sold for Rand 250m and if silver is found the parcel of land can be sold for Rand150m. MDG can, if they wish, pay Rand 750,000 for the right to conduct a three-day test exploration before deciding whether to purchase the parcel of land or not. Such three-day test explorations can only give a preliminary indication of whether significant metal deposits are present or not and past experience indicates that three-day test explorations cost Rand 250,000 and indicate that significant metal deposits are present 50% of the time. If the three-day test exploration indicates significant metal deposits then the chances of finding manganese, goid and silver increase to 3%,2% and 1% respectively. If the three-day test exploration fails to indicate significant metal deposits then the chances of finding manganese, goid and silver decrease to 0.75%,0.04% and 0.175% respectively. Note: Profit= Revenue - Cost a) Draw a decision tree for this problem b) What would you recommend MDG should do and why? Question four [20 marks] Recently you were assigned to manage a project for your company, In addition you have asked your team to estimate the amount of time that they would expect each of the activities to take. Their response is shown in the table below. a) Draw the network diagram for this project b) What is the expected completion time of the project? c) What is the probability of completing the project in 25 days d) What is the probability of completing the project in 19 days