SOLUTION: 2.Supplier of bicycles will make 200 bicycles available in the market per month when the unit price is $50, and 2,000 bicycles available per month when the unit price is $100. A)

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Question 1188051: 2.Supplier of bicycles will make 200 bicycles available in the market per month when the unit price is $50, and 2,000 bicycles available per month when the unit price is $100.
A) Find the (inverse) supply equation if it is known to be linear.
B) Find the price at which the supplier will stop supplying bicycle.
C) What happens to the quantity supplied of bicycles at the price of $40 ?
Answer by ikleyn(52784) About Me  (Show Source):
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Supplier of bicycles will make 200 bicycles available in the market per month when the unit price is $50,
and 2,000 bicycles available per month when the unit price is $100.
A) Find the (inverse) supply equation if it is known to be linear.
B) Find the price at which the supplier will stop supplying bicycle.
C) What happens to the quantity supplied of bicycles at the price of $40 ?
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They want you create a linear function of the form

    y = mx + b,

expressing the number of produced bicycles y as the function of unit price x.



        Start determine the slope coefficient m.



It is the ratio of increment of y (the number of bicycles) to the increment of unit price

    m = %282000-200%29%2F%28100-50%29 = 1800%2F50 = 36



So, the function is 

    y - 200 = 36*(x-50).      (1)



Thus question (A) is just answered.




(B)  In the formula (1), we should place y = 0 and find the corresponding value of x.

     You have then


         0 - 200 = 36*(x-50)

         36x - 36*50 = - 200

         36x = -200 + 36*50 = 1600

         x = 1600%2F36 = 44.44  dollars.    ANSWER


      At the price of $44.44, the producer will stop making bicycles.




(C)  To answer this question, simply substitute x= 40 into the formula.  You will get negative value for y.

     It means that at the price of $40 per bicycle, the producer will not produce bicycles.


     This answer is consistent with part (B).

Solved.

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