SOLUTION: Please help me to solve this. The supply function qs=f(p) for a product is quadratic.Three points which lie on the supply

Algebra ->  Functions -> SOLUTION: Please help me to solve this. The supply function qs=f(p) for a product is quadratic.Three points which lie on the supply       Log On


   



Question 881046: Please help me to solve this. The supply function qs=f(p) for a product is quadratic.Three points which lie on the supply function are (30,1500),(40,3600) and (50,6300). (i) determine the equation of the supply function. (ii)define restricted domain of the function. compute and interpret p intercept.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The quadratic has the form,
q=ap%5E2%2Bbp%2Bc
1500=a%2830%29%5E2%2Bb%2830%29%2Bc
1.900a%2B30b%2Bc=1500
.
.
.
Similarly,
2.1600a%2B40b%2Bc=3600
and
3.2500a%2B50b%2Bc=6300
Subtracting eq. 1 from eqs. 2 and 3,
2500a%2B50b%2Bc-900a-30b-c=6300-1500
1600a%2B20b=4800
4.80a%2Bb=240
and
1600a%2B40b%2Bc-900a-30b-c=3600-1500
700a%2B10b=2100
5.70a%2Bb=210
Substituting from eq. 4 into eq. 5,
70a%2B%28240-80a%29=210
-10a%2B240=210
-10a=-30
a=3
Then,
80%283%29%2Bb=240
b=0
and finally,
1600%283%29%2B40%280%29%2Bc=3600
c=-1200
.
.
.
q=3p%5E2-1200
.
.
.
0=3p%5E2-1200
3p%5E2=1200
p%5E2=400
p=20
20 is the lowest price of the item (usually it gets lower as quantity increases, in this case, it's more expensive to make more, that's counterintuitive)
graph%28300%2C300%2C-10%2C50%2C-500%2C4500%2C3x%5E2-1200%29