Math writing assignment

  Math  202  Category  W  Writing  Assignment  

  Part  1  

Suppose  you  start  your  own  business.    Determine  a  product  your  business  will   manufacture  or  produce.    Ideally,  the  chosen  product  will  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  $15  and  $310.     Part  2  

Suppose  total  fixed  costs  including  rent  and  utilities  for  your  business  are  $7,500   per  month.    Using  the  cost  per  unit  that  you  determined  in  part  1,  construct  a  linear  cost   function,   ,  for  your  product.    Suppose  you  can  afford  $150,000  in  total  costs  per  month,   how  many  units  can  you  produce?  

  Part  3  

Let    represent  the  quantity  of  units  of  your  product  demanded  each  month  and  let    represent  the  price  per  unit  which  you  sell  the  product  in  dollars.    Let  the  price  –  demand   equation  be   .    Construct  the  revenue  function,   ,  for  your  product.     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).    Next,  find  the  profit  function,   .  Determine  the  break  –   even  points  and  interpret  your  results.     Part  4  

Suppose  your  company  is  currently  producing  1,000  units  per  month.    Determine   the  marginal  cost  and  marginal  revenue  at  a  production  level  of    units  and  interpret   the  results.    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.     Report   Type  a  report  to  summarize  your  results  from  the  above  four  parts.    The  report  should   include  all  calculations  with  explanations  and/or  interpretations.    Also  include  in  this   report,  a  brief  summary  on  the  importance  of  marginal  analysis  to  business  operations.     This  assignment  is  worth  70  points  and  is  due  by  3pm  on  Monday,  April  6.