3. Kaylee’s Quality Quadratic Coffee Company (KQQCC) sells tall lattés for $3.75

Question

3. Kaylee’s Quality Quadratic Coffee Company (KQQCC) sells tall lattés for $3.75 each. Assume this is the only product KQQCC sells. KQQCC has fixed costs of $1,200 per month, and its actual cost to produce each latté is 95 cents.

A. (Six points.) KQQCC sells 2,000 lattés per month at the price of $3.75. Kaylee experimented with raising the price to $4.00 and found that sales dropped to 1,800 lattés per month. Assuming that this relationship between price and sales is linear, find a formula for the number of lattés she sells as a function of the price that she charges. Then find a formula for her revenue as a function of the price she charges, and determine the price she should charge to maximize revenue. Round your answer to the nearest five cents.


B. (Four points.) KQQCC’s profit is its revenue minus its total costs. Determine the price it should charge to maximize profit. 3. Kaylee’s Quality Quadratic Coffee Company (KQQCC) sells tall lattés for $3.75 each. Assume this is the only product KQQCC sells. KQQCC has fixed costs of $1,200 per month, and its actual cost to produce each latté is 95 cents.

A. (Six points.) KQQCC sells 2,000 lattés per month at the price of $3.75. Kaylee experimented with raising the price to $4.00 and found that sales dropped to 1,800 lattés per month. Assuming that this relationship between price and sales is linear, find a formula for the number of lattés she sells as a function of the price that she charges. Then find a formula for her revenue as a function of the price she charges, and determine the price she should charge to maximize revenue. Round your answer to the nearest five cents.


B. (Four points.) KQQCC’s profit is its revenue minus its total costs. Determine the price it should charge to maximize profit.

A. (Six points.) KQQCC sells 2,000 lattés per month at the price of $3.75. Kaylee experimented with raising the price to $4.00 and found that sales dropped to 1,800 lattés per month. Assuming that this relationship between price and sales is linear, find a formula for the number of lattés she sells as a function of the price that she charges. Then find a formula for her revenue as a function of the price she charges, and determine the price she should charge to maximize revenue. Round your answer to the nearest five cents.


B. (Four points.) KQQCC’s profit is its revenue minus its total costs. Determine the price it should charge to maximize profit.

Explanation / Answer

suppose Y1=2000, Y2=1800, X1=3.75,X2=4 HERE YREPESENTS NO. OF LATTES AND X REPRESENTS PRICE OF EACH

SO BY SOLVING LINER EQUATION WE GET

y= -800x+5000    (formula for the number of lattés she sells as a function of the price that she charges )

revenue R=rate*totale lattes

R=x*y

so R=5000x-800x2                  (formula for her revenue as a function of the price she charges)

for maximum revenue, we have to diffrenciate it with respect to x

so price she should charge to maximize revenue=5000/1600 =3.13$

B.

profit(P)=revenue(R)-cost(y*.95)

P=5000x-800x2 -(.95*(5000-800x))

P=5760x-800x2 -4750

diffrenciate it with respect to x,

the max price=5760/800$   =3.6$

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