Question

Q.8 Claire builds and sells birds houses .Claire makes n bird houses in a given week and sels them for 45-n T Dollars per bird house. Her weekly costs include a fixed cost of 280 plus $8 per bird house made. Assume that Claire sells all of the bird houses that she makes a) Write an equation to represent her total weekly cost b) Write an equation to represent her weekly revenue c) Write an inequality to express the conditions for which Claire will make a profit d) how many bird houses should Claire build each week in order to make a profit?

Answer 1

a)

C(n) = 280 + 8n 280 represents the fixed cost, while 8n represents the cost per bird house. R (n) = (45 - n)n 45 - n represents the price per bird house, while n represents the number of bird houses sold. R (n) > C (n) Revenue is greater than cost. R(n) > C(n) R(n) - C(n) > 0 (45 - n)n - (280 + 8n) > 0 45n - n^2 - 280 - 8n > 0 -n^2 + 37n - 280 > 0 n = -b plusminus squareroot b^2 - 4ac/2a n = -(37) plusminus squareroot (37)^2 - 4(-1) (-280)/2(-1) n = -37 plusminus squareroot 1369 - 1120/-2 n = -37 plusminus squareroot 249/-2 n = -37 + squareroot 249/-2 n = -37 squareroot 249/-2 n = 10.6 n = 26.4 n = 11 n = 26 11 lessthanorequalto n lessthanorequalto 26 She will make money if she makes between, and including, 11 and 26 birdhouses.

          280 represents the fixed cost, while 8n represents the cost per bird house.

b)

     45-n represents the price per bird house, while n represents the number of bird houses sold.

c)

     Revenue is greater than cost.

d)                 R(n) > C(n)

               R(n) - C(n) > 0

(45 - n)n - (280 + 8n) > 0

    45n - n² - 280 - 8n > 0

         -n² + 37n - 280 >0

             

            

She will make money if she makes between, and including, 11 and 26 birdhouses.