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# Tools for Business Decisions - Exercises 2

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### Tools for Business Decisions - Exercises 2

1. 1. 27C0100 Tools  for  Business  Decisions Exercises  2 kari.silvennoinen@student.hse.ﬁ
2. 2. Exercises • Exercises  are  due  always  on  the  following   Monday • You  can  return  them  by  dropping  them  to  the   return  box  on  the  1st  ﬂoor  at  Chydenia         kari.silvennoinen@student.hse.ﬁ 2
3. 3. Case  1  –  Merton  Truck  Company • The  case  is  available  on  the  website  and  in  the   binder  on  the  4th  ﬂoor  at  Chydenia • Maximum  group  size  is  4. • Due  on  February  4th • Return  to  the  box  on  1st  ﬂoor  at  Chydenia kari.silvennoinen@student.hse.ﬁ 3
4. 4. Exercise  set  1 • FormulaNon  and  a  graph  is  not  enough – Answer  the  ques9on  and  explain • Don’t  hide  the  answers  in  the  graph  or  Excel   cells – The  spreadsheets  and  graphs  jus9fy  your  result,   but  are  not  the  result.   kari.silvennoinen@student.hse.ﬁ 4
5. 5. Problem  1 • Two  ways  to  understand  the  problem – Both  are  jus5ﬁed • Are  the  plants  independent  or  not? – Independent:   • Diﬀerent  plants:  e.g.  Finland,  Sweden,  Estonia – Dependent:   • Parts  of  a  process:  e.g.  Sawing,  Construc5on,  Pain5ng • Big  part  of  problem  solving  is  to  understand  the   problem  and  its  dynamics   kari.silvennoinen@student.hse.ﬁ 5
6. 6. Problem  1 Independent Dependent (0,9),  f(x)  =  8700 (2,6),  f(x)  =  3600 kari.silvennoinen@hse.ﬁ 6
7. 7. 5 Problem  2 4 • Which  side  is  the   3 feasible  one  in  an   inequality? 2 • Test  a  point! 1 – (0,0)  is  usually  easy  and  a   x1-x2 ! 2 good  pick,  unless  on  the   0 1 2 3 4 line (0,0):  0  -­‐0  =  0  ≤  2 – If  fulﬁlls  the  inequality,   The  side  point  (0,0)  belongs  to  is  the   point  on  the  feasible  side   feasible  region  (ie.  above  the  line) kari.silvennoinen@hse.ﬁ 7
8. 8. Problem  2 8 6 4 x2 2 0 x1 ! x2 ! 2 ! 3x1 + 6x2 ! 3 -2 4x1 ! 3x2 ! 1 0 2 4 6 8 10 x1 kari.silvennoinen@student.hse.ﬁ 8
9. 9. Problem  3 • Choose  your  c1  values  carefully. – Many  evaluated  points  like  -­‐1,   6 0,  1,  2,  … 5 – …and  missed  the  cri5cal  value   at  0,5 4 c1 (x) 3 • If  the  objec5ve  func5on’s   2 coeﬃcient  matches  that  of  a   constraint: 1 – Whole  segment  is  op5mal! 0 (not  just  the  two  end  points  of   that  segment) 0 1 2 3 4 5 6 x kari.silvennoinen@hse.ﬁ 9
10. 10. MulN-­‐period  planning The  Silver  Star  Bicycle  Company  will  be   manufacturing  men’s  and  women’s  models  for  its   10  speed  bicycles  during  the  next  2  months.   Management  wants  to  develop  a  producNon   schedule  indicaNng  how  many  bicycles  of  each   model  should  be  produced  in  each  month.   Demand  forecasts  call  for  150  men’s  and  125   women’s  models  to  be  shipped  during  the  ﬁrst   month  and  200  men’s  and  150  women’s  during   the  second  month kari.silvennoinen@student.hse.ﬁ 10
11. 11. Silver  Star  Bicycle  Company Model Produc5on   Labor  requirements  (hrs) Current   Costs Manuf. Assembly Inventory Men’s \$  120 2.0 1.5 20 Women’s \$  90 1.6 1.0 30 Last  month  the  company  used  a  total  of  1000  hours  of  labor.  Company’s   policy  will  not  allow  the  total  hours  of  labor  to  increase  or  decrease  by   more  than  100  hours  from  month  to  month.  The  company  charges   inventory  2%  of  the  produc5on  cost.  The  company  would  like  to  have  at   least  25  units  of  each  model  at  the  end  of  the  2  months. What  is  the  minimum  cost  produc5on  schedule? kari.silvennoinen@student.hse.ﬁ 11