Question

Pack-em-in real estate is building a new housing development. The more houses it builds, the less people will be willing to pay, due to the crowding and smaller lot sizes. In fact, if it builds 30 houses in this particular development, it can sell them for $260,000 each, but if it builds 80 houses, it will only be able to get $160,000 each. Obtain a linear demand equation. (let p be the price of a house and q the number of houses.)

a) p = −2,000q + 320,000
b) p = −2,500q + 300,000
c) p = −1,500q + 280,000
d) p = −2,000q + 300,000

Answer 1

The linear demand equation for this scenario is p = -2000q + 320000. We have two points that lie on the line: (30, 260000) and (80, 160000). To obtain a linear demand equation, we can use two points on the line and calculate the slope and y-intercept.

Step-by-step explanation:

To obtain a linear demand equation, we need to find the slope and the y-intercept. We have two points that lie on the line: (30, 260000) and (80, 160000). The formula for finding the slope is:

m = (y2 - y1) / (x2 - x1) = (160000 - 260000) / (80 - 30) = -100000 / 50 = -2000

The y-intercept is the price when the quantity is 0. We can use the point (30, 260000) to calculate it: y = mx + c -> 260000 = -2000(30) + c -> c = 260000 + 60000 -> c = 320000

Putting it all together, the linear demand equation is: p = -2000q + 320000.