Respuesta :
Let p be the price and q be the quantity of hamburgers.
a)When price is 0, every one takes 2 hamburgers so, q=120*2 = 240
When p=4, q =0
Hence slope of demand line =[tex]\frac{240-0}{0-4} = \frac{236}{-4} = -60[/tex]
Then the demand equation is q=-60p+b ( assume p on x-axis and q on y-axis like y=mx+b)
To find b, we plugin the point (240,0)
240 = m*0+b
b= 240
Hence demand equation is q=240-60p.
b) To find p in terms of q,we will solve for p from demand equation.
q-240 = -60p
[tex]\frac{q-240}{-60} = p[/tex]
[tex]p=\frac{q}{-60} -\frac{240}{-60}[/tex]
[tex]p=4-\frac{q}{60}[/tex]
c) Revenue = price * quantity
= [tex]p*(240-60p) = 240p-60p^{2}[/tex]
Hence it is quadratic equation.
d) [tex]R=-60*(p^{2} -4p)[/tex]
= [tex]-60(p^{2}-4p+4-4)[/tex]
= [tex]-60((p-2)^{2} -4)[/tex]
= [tex]-60(p-2)^{2}+240[/tex]
The above equation is a inverted u-shape parabola.
Hence maximum revenue occurs at vertex that is at p=2.
