Question

Suppose the supply and demand for a certain textbook are given by ​supply: P=(1/2)q ^2 and demand P=(-1/2)q^2+30

where p is the price and q is the quantity. Find the demand quantity and the supply quantity at a price of

​$25

1)The number of books that are demanded at a price of $25 is........

and the number of books supplied at a price of ​$25 is......

​(Round to the nearest whole number as​ needed.)

Answer 1

SOLUTION:

From given data,

Suppose the supply and demand for a certain textbook are given by ​supply: P=(1/2)q ^2 and demand P=(-1/2)q^2+30

where p is the price and q is the quantity. Find the demand quantity and the supply quantity at a price of​ $25

1)The number of books that are demanded at a price of $25 is

Given supply P=(1/2)q²

demand P=(-1/2)q² +30

P = $25

supply

25 = (1/2)q²

q² = 50

demand

P=(-1/2)q² +30

25=(-1/2)q² +30

-5 = (-1/2)q²

q² = 10

Therefore the number of books that are demanded at a price of $25 is 3.16 and the number of books supplied at a price of $25 is 7.07