Math, asked by euroqureshi, 7 months ago

The supply function qs = f (p) for a product is quadratic. Three points which lie on the supply function are (60, 2750), (70, 6000) and (80, 9750). a) Determine the equation for the supply function b) Make any observation you can about the restricted domain of the function c) Compute and interpret the p intercept. d) What quantity will be supplied at a price of $75

Answers

Answered by amitnrw
2

Given  :   The supply function qs = f (p) for a product is quadratic. Three points which lie on the supply function are (60, 2750), (70, 6000) and (80, 9750).  

To find :  a) Determine the equation for the supply function b) Make any observation you can about the restricted domain of the function c) Compute and interpret the p intercept. d) What quantity will be supplied at a price of $75

Solution:

let say

f(p) = ap² + bp  + c

Three points  lie on the supply function are (60, 2750), (70, 6000) and (80, 9750).

=> f(60) = a(60)² + b(60) + c  = 2750    Eq1

f(70) = a(70)² + b(70) + c  = 6000        Eq2

f(80) = a(80)² + b(80) + c  = 9750        Eq3

Eq2 - Eq1

=>  1300a  + 10b  =  3250

Eq3 - Eq2

=>  1500a + 10b  = 3750  

=> 200a  = 500

=> a = 2.5  

1500a + 10b  = 3750  

=> 1500(2.5) + 10b = 3750

=> b = 0

a(60)² + b(60) + c  = 2750

=> 2.5(60)² + 0 + c = 2750

=> c = -6250

f(p) = (2.5)p² - 6250

p intercept = 50  as  f(50) =  0  

Domain  p ≥ 50   ∵  f(p) ≥ 0  

What quantity will be supplied at a price of $75

=> f(75) = 2.5(75)² - 6250

= 7812.5

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