Answer:
(a) The price for a revenue of $18,750 is $239.2.
(b) They sold 710 colonial houses and 2130 ranch houses
Step-by-step explanation:
(a) If the weekly revenue is defined as
[tex]r=2p^2+400p[/tex]
then the price must be calculated as:
[tex]r=2p^2+400p=18750\\\\2p^2+400p-18750=0[/tex]
The roots of this function are
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{-400 \pm \sqrt{400^2-4*2*(-18750)}}{2*2}\\ \\x=\frac{-400 \pm 556.78}{4}\\ \\x_1=-39.2\\x_2=239.2[/tex]
The first root is negative, so it is not a real solution. So the second root is the answer.
The price for a revenue of $18,750 is $239.2.
(b) Last year they sold three times as many ranch models (Hr) as they did colonial models (Hc):
[tex]H_r=3*H_c[/tex]
The total amount of houses sold (colonial + ranch) is 2840
[tex]H_c+H_r=2840\\H_c+3*H_c=2840\\4*H_c=2840\\H_c=2840/4=710\\\\H_r = 3*H_c=3*710=2130[/tex]
