Pack-Em-In Real Estate is building a new housing development. The more houses it

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 20 houses in this particular development, it can sell them for $640,000 each, but if it builds 60 houses, it will only be able to get $480,000 each. Obtain a linear demand equation. HINT [See Example 3.] (Let p be the price of a house and q the number of houses.)

I know the DEMAND EQUATION is q(p)= -4000p+720,000 and the REVENUE EQUATION is r(p)= -4000p2 +720,000p

But I for some reason can't think of it the other way.

Question:

p(q)=

Explanation / Answer

The demand curve of a product shows how the price and quantity are related. Here too we have been given the price corresponding to a given quantity of products. At different quantities the same item has a different. this is because abundance causes people to value a product less, while scarcity causes them to value it more.

So a general linear equation is given as y = mx + c ; where y and x are variable, m is the proportionality factor and c is a constant.

Here our y and x are the price and quantity. now let us find the m and c for it.

in the first case for x=20, y=$640,000

so 640,000 = 20*m + c --------------------- eqn 1

and in the second case for x = 60, y=$480,000

so 480,000 = 60*m + c ----------------------eqn 2

Subtracting eqn 2 from 1

160,000 = -40m

or m = 4,000

So the eqn is p(q) = -4000q + c

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.