Question

Ack-em-in has another development in the works. If it builds 60 houses in this development, it will be able to sell them at 600,000 each, but if it builds 100 houses, it will get only480,000 each. Obtain a linear demand equation. (Let p be the price of a house and q the number of houses.)

Answer 1

A linear demand equation representing the price-to-quantity relationship for houses in the given development is p = -3,000q + 780,000.

Step-by-step explanation:

To derive the linear demand equation, we have two points that define the demand relationship: (60, 600,000) and (100, 480,000), where the first number in each pair is the quantity (q) and the second is the price (p). Using the slope formula, Δp/Δq = (p2 - p1) / (q2 - q1), we get the slope (m) as:

m = (480,000 - 600,000) / (100 - 60) = -120,000 / 40 = -3,000.

Now, we can write the equation in the point-slope form: p - p1 = m(q - q1), using one of the points for p1 and q1:

p - 600,000 = -3,000(q - 60).

p = -3,000q + 780,000.

This equation represents the relationship between the price of houses and the quantity available in this housing development scenario, reflecting a typical downward-sloping demand curve. It implies that for every additional house built, the price decreases by $3,000, starting from a maximum price of $780,000 when no houses are built.