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23 March, 03:26

Suppose the supply and demand for a certain textbook are given by supply: p equals one fourth q squared comma demand: p equals negative one fourth q squared plus 30 comma where p is the price and q is the quantity. Find the demand quantity and the supply quantity at a price of $15.

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  1. 23 March, 03:44
    0
    The number of books that are demanded at a price of $15 is 8

    The number of books supplied at a price of $15 is 8

    Explanation:

    Given the supply and demand function of the textbook, p = 1/4 q2, and p = - 1/4 q2 + 30 respectively, where p and q is the price and quantity respectively,

    The quantity supplied at the price of $15 would be:

    p = 1/4 q2

    p = ¼ * q2

    p = q2/4

    15 = q2/4

    15 * 4 = q2

    60 = q2

    q = 7.75 ≈ 8 (square root of 60)

    The quantity demanded at the price of $15 would be:

    p = - 1/4 q2 + 30

    p = - q2/4 + 30

    p - 30 = - q2/4

    (p - 30) (4) = - q2

    (15 - 30) (4) = - q2

    ( - 15) (4) = - q2

    - 60 = - q2

    60 = q2

    q = 7.75 ≈ 8 (square root of 60)
  2. 23 March, 03:46
    0
    the demand quantity and the supply quantity at a price of $15 is 8 units

    Explanation:

    Supply, P = 1/4 Q²

    Demand, P = - 1/4 Q²+30

    If P = 15

    Quantity Demanded will be 15 = - 0.25Q²+30;

    if we move 30 across the equality sign.

    Therefore - 0.25Q²=-15; divide both sides by - 0.25;

    Q² = 60, Q = 7.746, approximately 8 units

    Quantity Supplied will be 15 = 1/4 Q², dividing both sides by 1/4

    Q² = 60, Q = 7.746, approximately 8.
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