PackEM In Real Estate is building a new housing development

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 40 houses in this particular development it can sell them for $200,000 each, but if it builds 7o houses it will only be get $140,000 each create a linear demand equation (p) for the price of homes as function of the quantity of homes (q). create a Revenue function How many houses should Pack-EM-IN build to get the largest revenue? What is the largest possible revenue?

Solution

Here we get two points (40,200000) and (70,140000)

Slope= (200000-140000)/(40-70) = 60000/-30= -20000

Using slope point form

p-200000=-2000(q-40)

p= -2000x + 80000+200000=-2000q + 280000

b. Revenue ,R= p * q= (-2000q+280000)q= -2000q²+280000q

c. To find number of houses that maximizes the revenue,we have to find the vertex

vertex,q= -280000/2(-2000)= 70

d. maximum revenue is

-2000(70²)+ 280000(70)=$9800000