Training Major Bill Bligh, Director of the Army War College’s new six-month attaché training program, is concerned about how the 20 officers taking the course spend their time while in his charge. Major Bligh recognizes that there are 168 hours per week and thinks his students have been using them rather inefficiently. Bligh lets: X1 = number of hours of sleep needed per week X2 = number of personal hours X3 = number of hours of class and studying X4 = number of hours of social time off base He thinks that students should study 30 hours a week to have time to absorb the material. This is his most important goal. Bligh feels that students need at most 7 hours of sleep per night on average and that this goal is number 2. He believes that goal number 3 is to provide at least 20 hours per week of social time. Formulate this goal programming problem Solve with the software (lindo or excel) of your choice. Solution Total hours x= 168 hours è 7days X = 1 week = 168 hours = 7 days + 7 nights X1 = number of hours of sleep needed per week Based on goal number 2 students need at most 7 hours of sleep per night on average So, X1=7*7 = 49 Hours per week X3 = number of hours of class and studying 30 hours a week to have time to absorb the material X3 = 30 hours per week X4 = number of hours of social time off base that goal number 3 is to provide at least 20 hours per week of social time. X4 = 20 hours per week X2 = number of personal hours 69 X1+X2+ X1+X2 = X X=168 X1=49 X2=? X3=30 X4=20 X2 = x-(X1+X2+X3) X2 = 168-(49+30+20); X2 = 168-99; X2 = 99 MAX 2 X4 + S5 ST X1 + S1 = 168 S1- 0.5 X1 - X2 - S2 = 0 2 X1 + S2 - 0.5 X2 - X3 - S3 = 0 2 X2 + S3 - 0.5 X3 - X4 - S4 = 0 2 X3 + S4 - 0.5 X4 - S5 = 0 END.

1. What are three types of Why are fossils important to scientists? What are three types of
evidence that support evolutionary theory? What is the role of natural selection in the process
evolution? Explain the variations in the beaks of Darwin's finches and then importance. What
is meant "survival of the fittest"? How does the environment
Solution
Ans 1. The preservation of fossils are known as fossilization which are further subdivided into
five types,which are: 1) Insect preserved in amber, 2) Petrified wood (Premineralization), 3) Cast
and mold of a calm shell 4) Pyritized ammonite and 5) Compression fossil of fern.
Ans 2. Fossils are the most valuable source of information available on earth which provide
useful information about the Earths history. They tell us about the organisms which lived on the
earth from the time of oldest fossils to till date. Scientists who want to learn about earth dig the
fossils. Hence they are important for scientists. Most of the fossils are found in the layers of rock.
Ans 3. The types of evidences which support evolution theory are : 1) Fossil record 2)
Geographic distribution of living species 3) Homologous structures of living organism 4)
Embryology.
Ans 4. Evolution is a slow process where different species join the world and live together.
Natural selection is how nature selects the fittest to survive. Natural selection determines the
direction of evolution. If animal is mutated and its mutation is beneficial for itys survival then in
such case the mutation would be inherited to the later generation. Natural selection would give a
better condition for the animals to survive in the environment.
Ans 5. The variation was observed at galapagos island, the beaks of different species varied on
different island. This variation in the beaks was due to the availability of food on that island. The
finches which ate large nuts had strong beaks to break open the nuts whereas on the contrary the
one who ate small nuts had beaks for cracking the nuts.This variation proved as vital feature for
his theory of Natural selection.
Ans 6. Survival of the fittest is a phrase coined by charles darwin considering his theory of
natural selection. As per the theory the one which is suitable to adapt to the environment are
more likely to survive and produce progeny than the ones which adapt to lesser extent.