Question

A business finds that the quantity demanded by consumers changes with the price at a rate of D'(p)= -3000/p^2

1.) Find the demand function if the business knows that 591 units of the product are demanded when the price is $8.

2.) What price should the business charge if it wants consumers to demand 1050 units of its product?

Please show all work.

Answer 1

1) We are given the rate of change of the quantity demanded. We can find the quantity demanded just by integrating the rate of change of quantity demanded.

The above equation gives the demand function. In order to find the value of C, put D(p)=591 and p =$8

Now substitute the value of C back into the demand function

Therefore, the above equation gives demand function if the business knows that 591 units of the product are demanded when the price is $8.

b) Put Q(p) = 1050 units in the demand function in order to get the price

Therefore, price = $3.60.

Please put a thumbs up if you found this answer helpful. Thanks!