Math Writing Assignment

  Math  202  Marginal  Analysis  Writing  Assignment  

Instructions   Your  assignment  is  to  write  an  original  report  that  gives  essay  –  style  answers  to  the  

questions  posed  below.  Be  sure  to  address  every  point  of  discussion.  The  report  should   include  explanations  and  interpretations  for  all  values  with  units  labeled  appropriately.   Your  conclusions  should  make  sense  in  the  context  of  the  scenario  and  should  be  consistent   throughout  the  paper  (make  sure  you  don’t  contradict  yourself).    

This  assignment  is  worth  100  points  and  is  due  Monday,  Nov.  28  by  5pm.  If  your   paper  is  submitted  by  the  early  deadline  (5pm  Wed,  Nov.  16)  you  will  receive  10  points   extra  credit.  If  your  paper  is  submitted  by  the  late  deadline  (5pm  Wed,  Nov.  30)  you  will   receive  a  10-­‐point  penalty.  No  papers  will  be  accepted  after  November  30.  Papers  should   be  reasonably  formatted  and  will  be  submitted  online  through  MyMathLab  writing  space.   You  do  not  need  to  attach  your  scratch  work.  

  Prompt  

Suppose  you  start  your  own  business.  Determine  a  product  your  business  will   manufacture  or  produce.  The  chosen  product  should  be  a  general  description,  for  example   a  smartphone,  not  a  specific  brand  or  item,  for  example  an  iPhone  6.  Do  some  informal   research  to  determine  a  reasonable  cost  of  producing  one  unit  of  the  product.  The   restriction  on  this  is  that  the  cost  per  unit  must  be  between  $10  and  $140.  

Suppose  total  fixed  costs  including  rent  and  utilities  for  your  business  are  $4000  per   month.  Using  the  cost  per  unit  that  you  determined,  construct  a  linear  cost  function,  !(!),   for  your  product.    

Let  !  represent  the  quantity  of  units  of  your  product  demanded  each  month  and  let   !  represent  the  price  per  unit  at  which  you  sell  the  product,  in  dollars.  Let  the  price  –   demand  equation  be  ! = !(!) = 12000 − 75!.  Determine  the  feasible  range  of  units   demanded  per  month  (i.e.  what  is  the  smallest  number  of  products  you  could  feasibly  sell   and  what  is  the  largest  number  of  products  you  could  feasibly  sell  in  a  month).  Construct   the  revenue  and  profit  functions,  ! !  and  ! ! ,  for  your  product.  Determine  the  break  –   even  points  and  interpret  your  results.  

Suppose  your  company  is  currently  producing  3,000  units  per  month.  Determine  the   cost,  revenue,  and  profit  at  3,000  units.  Determine  the  marginal  cost,  marginal  revenue  and   marginal  profit  at  a  production  level  of  3,000  units  and  interpret  the  results.  According  to   the  price  –  demand  equation,  at  what  unit  price  are  you  selling  your  product  if  demand  is   3,000  units  per  month?  Write  a  function  for  the  elasticity  of  demand  !(!)  and  determine   whether  the  demand  is  elastic,  inelastic,  or  has  unit  elasticity  at  this  price.  Discuss  how   increasing  or  decreasing  the  price  would  affect  the  revenue.  

Based  on  the  analysis  you  have  done  so  far,  should  you  increase  or  decrease   production?  Justify  your  answer.  Finally,  determine  the  optimal  production  level  that  will   maximize  profits  and  explain  why  you  know  this.  What  is  the  maximum  profit?  Determine   the  revenue  and  cost  for  the  optimal  production  level.  At  what  price  should  you  sell  each   unit  so  that  you  can  maximize  profit?  Draw  some  conclusions  about  your  business’s   optimal  operations.  You  should  conclude  your  report  with  a  brief  summary  on  the   importance  of  marginal  analysis  to  business  operations.