Question

A certain bakery has found that the daily demand for bran muffins is StartFraction 9600 Over p EndFraction 9600 p ​, where p is the price of a muffin in cents. The daily supply is 44pminus−200200. Find the price at which supply and demand are equal.

Answer 1

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

$\dfrac{9600}{p}$

where p is the price of a muffin in cents.

Supply function is given by

$44p-200$

We need to find the price at which supply and demand are equal.

so, it becomes,

$\dfrac{9600}{p}=44p-200\\\\9600=(4p-200)p\\\\9600=4p^2-200p\\\\2400=p^2-50p\\\\p^2-50p-2400=0\\\\p=80,-30$

We discarded p = -30 as price cannot be negative.

so, the price would be $80 at which supply and demand are equal.

Answer 2

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.