Answer: The price would be $80 at which supply and demand are equal.
Step-by-step explanation:
Since we have given that
Demand function is given by
[tex]\dfrac{9600}{p}[/tex]
where p is the price of a muffin in cents.
Supply function is given by
[tex]44p-200[/tex]
We need to find the price at which supply and demand are equal.
so, it becomes,
[tex]\dfrac{9600}{p}=44p-200\\\\9600=(4p-200)p\\\\9600=4p^2-200p\\\\2400=p^2-50p\\\\p^2-50p-2400=0\\\\p=80,-30[/tex]
We discarded p = -30 as price cannot be negative.
so, the price would be $80 at which supply and demand are equal.
Answer:
Step-by-step explanation:
The bakery found out that the demand is
D = 9600 / p
Where P is the price of muffins in cents
Daily supply is give as
S=4p — 200 ( I believe it is a typo error, and that is why I used 4p - 200, due to the experience I have with brainly site.)
We want to find the price at which the demand is equal to the supply
It is a very straight forward questions
Demand. = Supply
Then,
D = S
9600 / p = 4p - 200
Cross multiply
9600 = 4p² - 200p
Rearrange to form quadratic equation
4p² - 200p - 9600 = 0
Divide through by 4
p² - 50p - 2400 = 0
Check attachment for solution using formula method to solve quadratic equation
Using factorization
p² - 80p + 30p - 2400 = 0
p(p-80) + 30(p-80) = 0
(p+30)(p-80) = 0
So, it is either p+30 = 0. Or p-80=0
p = -30 or p = 80
Since the price can't be negative,
We are going to discard the negative price.
Then, the price is 80cents per muffins.
