Application Problem

1)      Stephanie makes and sells jewellery for the gift shop at the museum. She makes n necklaces in a given week and sells them for 25-n dollars per necklace. Her costs include a fixed cost of $55 plus $3.50 per necklace made. Assume that Stephanie sells all of the necklaces she made…

a)      Write an equation to represent her total weekly cost.

               Let n be the given number of necklaces made in a week.

               C(n)= fixed cost + variable cost

b)     Write an equation to represent her total weekly revenue.

          R(n)= price per necklace x number of necklaces made per week

c)     Write an inequality to express the conditions which Stephanie will make a profit.

          Stephanie will make a profit if her revenue is greater than her costs.

          R(n) > C (n)    OR      R(n) – C(n) = 0

d)     How many necklaces should Stephanie make each week in order to make a profit?

          1)      Graph the functions on the same graph     

          2)      Compare the graphs visually

Y= 55+3.5n      

.: Stephanie should make between 9 and 13 necklaces each week because the graph of R(n) is above graph C(n) between x= 3 and x= 19.

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