6. A project requires the completion of eight activities. Th…

6. A project requires the completion of eight activities. The immediate predecessors (predecessors), normal activity time in weeks (normal time), maximum crashing time in weeks (max crash time), and per week crashing cost (crash cost) are shown in the table below. Activity 1 2 3 4 5 6 7 8 predecessors none none none 1,2 1,2,3 3 5,6 4,7 normal time 6 8 7 9 5 7 4 6 max crash time 3 2 3 4 1 2 2 3 crash cost $650 $550 $700 $465 $500 $385 $720 $810 Using the “normal time” values, find and report the early start times, early finish times, late start times, late finish times, and slack for each activity. Identify the critical path and project completion time.

Consider a locational cost-profit-volume analysis problem wh…

Consider a locational cost-profit-volume analysis problem where fixed and variable cost information is provided for three location alternatives: A, B, and C, where A has the lowest fixed cost and the highest variable cost and B has the highest fixed cost and the lowest variable cost. Suppose that you compute the breakeven point for alternatives A and C, as well as the breakeven point between alternatives B and C. Carefully explain under what circumstances (and the reason) that it would also be necessary to compute the breakeven point for alternatives A and B.

A company wants to develop a location-distribution plan. The…

A company wants to develop a location-distribution plan. They are considering up to five plant locations (Jacksonville, Tallahassee, Ocala, Tampa, Miami) to supply three warehouse distribution center locations (Lake City, Orlando, West Palm). The selected plants will ship units to meet demand at the warehouses. The table below provides relevant cost information, plant capacities, DC capacities, and warehouse demands.     Per unit shipping costs     Warehouse   Jacksonville Tallahassee Ocala Tampa Miami   Demand Lake City $3.90 $3.30 $2.80 $4.90 $7.10   3500 Orlando $4.70 $5.90 $1.90 $4.20 $6.30 3900 West Palm $6.20 $6.80 $5.50 $3.50 $2.70   4100                 Plant capacity 5100 6500 3800 5400 3900   Plant fixed cost $15,000 $12,500 $20,000 $24,000 $19,000     Fixed costs for plants are only realized if they are opened/selected. Prepare an integer linear programming model that, when solved, will determine the plants to be opened and a shipment plan that will meet the demand at the warehouses exactly yet not exceed the capacity limits of the plants. An additional restriction for each selected plant is that it must ship at least 80% of its available capacity. The goal is to minimize the total fixed costs of plants  plus the total variable (per unit) costs of shipment.

Read the following short article about language. 1.  Choose…

Read the following short article about language. 1.  Choose five (5) of the words in bold/underlined and explain what they mean in your own words–no dictionaries nor internet.   2.  Then explain what the 2 underlined sentences mean in your own words. 6,000 languages: an embattled heritage By Ranka Bjelja-Babic       Are the vast majority of languages doomed to die out in the near future? Specialists reckon that no language can survive unless 100,000 people speak it. Half of the 6,000 or so languages in the world today are spoken by fewer than 10,000 people and a quarter by less than 1,000. Only a score is spoken by hundreds of millions of people       The death of languages is not a new phenomenon. Languages usually have a relatively short life span as well as a very high death rate. Only a few, including Basque, Egyptian, Chinese, Greek, Hebrew, Latin, Persian, Sanskrit and Tamil have lasted more than 2,000 years.       What is new, however, is the speed at which they are dying out. Europe’s colonial conquests caused a sharp decline in linguistics diversity, eliminating at least 15 percent of all languages spoken at the time. Over the last 300 years, Europe has lost a dozen, and Australia has only 20 left of the 250 spoken at the end of the 18th century. In Brazil, about 540 (three-quarters of the total) have died out since Portuguese colonization began in 1530.       The rise of nation-states, whose territorial unity was closely linked to their linguistic homogeneity, has also been decisive in selecting and consolidating national languages and sidelining others. By making great efforts to establish an official language in education, the media and the civil service, national governments have deliberately tried to eliminate minority languages.       This process of linguistic standardization has been boosted by industrialization and scientific progress which have imposed new methods of communication that are swift, straightforward and practical. Language diversity came to be seen as an obstacle to trade and the spread of knowledge. Monolingualism became the ideal.       More recently, the internationalization of financial markets, the dissemination of information by electronic media and other aspects of globalization have intensified the threat to “small” languages. A language not on the Internet is a language that “no longer exists” in the modern world. It is out of the game. It is not even used in business.       The effects of the death of languages are serious for several reasons. First of all, it is possible that if we all ended up speaking the same language, our brains would lose some of their natural capacity for linguistic inventiveness. We would never be able to plumb the origins of human language or resolve the mystery of “the first language.” As each language dies, a chapter of human history closes.       Multilingualism is the most accurate reflection of multiculturalism. The destruction of the first will inevitably lead to the loss of the second. Imposing a language without any links to a people’s culture and way of life stifles the expression of their collective genius. A language is not only used for the main instrument of human communication. It also expresses the world vision of those who speak it, their imagination and their ways of using knowledge. Thus, the preservation of languages no matter how minor is an urgent matter.