Answer:
The demand function is p= (-2.1)*q + 15.3
Explanation:
The supply function for honey is p=S(q)=0.4*q+2.8, where p is the price in dollars for an 8-oz container and q is the quantity in barrels. The equilibrium price is $4.80. So, the equilibrium quantity is:
4.80=0.4*q+2.8
Solving:
4.80 - 2.8=0.4*q
2=0.4*q
2÷0.4= q
5=q
The demand function, assuming it is linear, is p=m*q+b
The equilibrium quantity is 5 barrels and the equilibrium price is $4.80; and the demand is 4 barrels when the price is $6.90. So:
[tex]\left \{ {{4.80=m*5+b} \atop {6.90=m*4+b}} \right.[/tex]
Isolating the variable "b" from the first equation, you get:
4.80 - m*5= b
Replacing the previous expression in the second equation you get:
6.90=m*4 + 4.80 - m*5
6.90 - 4.80=m*4 - m*5
2.1= (-1)*m
2.1÷(-1)= m
-2.1=m
Replacing the value of "m" in the expression 4.80 - m*5= b you get:
4.80 - (-2.1)*5= b
Solving you get:
15.3= b
So, the demand function is p= (-2.1)*q + 15.3
