MATH 106 Finite Mathematics 2172-OL1-6380-V1Page 1 of 10MATH 106 FINAL EXAMINATIONThis is an open-book exam. You may refer to your text and other course materials as you work on the exam and you may use a calculator. You must complete the exam individually. Neither collaboration nor consultation with others is allowed. Use of instructors solutions manuals or online problem solving services in NOT allowed.Record your answers and work on the separate answer sheet provided.There are 25 problems.Problems #112 are Multiple Choice.Problems #1315 are Short Answer. (Work not required to be shown)Problems #1625 are Short Answer with work required to be shown.MULTIPLE CHOICE1. 2. The Benjamin Banneker Astronomics Company employs physicists and astronomers. According to company data a physicist does 2 observations and 3 calculations per day whereas an astronomer does 6 observations and 3 calculations per day. The company needs enough staff on hand for at least 24 observations per day and at least 18 calculations per day. A physicist makes $100 per day and an astronomer makes $90 per day. The company wants to minimize daily labor costs in order to get a research grant. Let x represent number of physicists and y represent number of astronomers.1. Identify the daily production constraint for observations:1. _______A. 2