SOLUTION: The consumers will demand 28 units when the price of a product is $44, and 47 units when the price is $30. Find the demand function (express thr price p in terms of the quantity q)

Question 939571: The consumers will demand 28 units when the price of a product is $44, and 47 units when the price is $30. Find the demand function (express thr price p in terms of the quantity q), assuming it is linear. p=
Answer by laoman(51) (Show Source): You can put this solution on YOUR website!
For this question, the demand and price function has a linear correlation
Using the linear equation, q=m*p+ c
where q is quantity demanded, m is the gradient, p is the price and c is the constant
Substituting into the formula
From the first clause, 28 =44m +c ------eqn1
From the second clause, 47 =30m + c -----eqn2
Solve the two equations for m and c,
i.e subtract eqn 2 from 1,
28-47=44m-30m+c-c
-19 = 14m
m = -19/14
Also to find c, from eqn1
c=28-44*m=28-44*-19/14 = 614/7
Now, substituting m and c into the linear eqn, q = (-19/14) * p + 614/7
We need to make p the subject of formulan for our final answer,
Multiply first althrough by 14
14q = -19p + 1228
Rearranging
-19p =14q-1228
Dividing althrough by -19

QED
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