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Sum Questions

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Department
Mathematics
Course
MAT135H1
Professor
All Professors
Semester
Summer

Description
Sum  Questions-­‐  optimization     Knowledge  Summary:     Similar  to  optimization  questions  (refer  to  Optimization  Knowledge  Summary),  but  here  we  are   looking  for  the  smallest  value  of  a  function  subject  to  some  kind  of  constraint.       Examples:     1) The  product  of  two  positive  numbers  is  25.    What  is  the  smallest  possible  value  of  their   sum?     ▯▯ 𝑥𝑦 = 25à  𝑦 = ▯ ,  put  this  into  𝑆 = 𝑥 + 𝑦     𝑆 = 𝑥 + 𝑦 = 𝑥 + ▯▯ ,  take  first  derivative:  𝑆 = 1 − ▯ ▯▯ ,  set  to  0  and  solve:   ▯ ▯ ▯    0 = 1 − ▯▯   ▯ ▯   = 1   ▯ ▯  25 = 𝑥   ▯                   𝑥 = 25 = 5   𝑆 = 𝑥 + ▯▯ = 5 + ▯▯ =10.    Therefore,  the  smallest  possible  value  of  their  sum  is  10.   ▯ ▯   Past  Test  Questions:     Year:  2002   Question:  11   The  product  of  two  positive  numbers  is  16.    What  is  the  smallest  possible  value  of  their  sum?            
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