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At Disneyland they sell candy to fundraise for outside charities. They sell about 5500 candy bars at a profit of $0.75/each. Each $0.50 increase in the price will increase the profit of each candy bar by $0.50. However, they will sell about 1000 fewer candy bars. 

 

A.) whAt is the profit for Disney if the profit is $0.75 per candy bar?

for my answer I got 5500(.75)= $4125

 

b.) find an equation for this model of the profit disney makes if they increase the price of each candy

bar by $0.50 “x” amount of times

my answer: p(x)=4500(.75)+0.50x

 

c.) use your model to determine the profit if the price per candy bar is increased by $1.00

my answer: 4500=0.50(2)+0.75

4500=$1.75

p=$2571.429

 

d.) what price increase will bring the school the highest profit? 

Couldn’t figure this one out 

 

E.) what is the highest profit? 

Same with this one 

Guest Nov 28, 2018
edited by Guest  Nov 28, 2018
 #1
avatar+14579 
+1

I'd say you got  A correct

 

B   (5500-1000x)   is the candy bars they will sell

        (5500-1000x)(.75 + .50 x )  is the profit

        4125 + 2750 x - 750x - 500x^2 = profit

         -500 x^2 + 2000x + 4125 = profit

 

C 1 dollar is   50 (2)    x= 2

       -500(2^2) + 2000(2) + 4125 = $6125

 

D This equation is an upside down parabola

        max = -b/(2a)  =  -2000/-1000  = 2 = x

 

E the profit will be as found for x = 2   in C

 

Here is the graph  :

 

ElectricPavlov  Nov 28, 2018
 #2
avatar+92814 
+1

At Disneyland they sell candy to fundraise for outside charities. They sell about 5500 candy bars at a profit of $0.75/each. Each $0.50 increase in the price will increase the profit of each candy bar by $0.50. However, they will sell about 1000 fewer candy bars. 

 

A is correct

 

B    Let x be the number of .50 increases....and for each N, they sell 1000 fewer candy bars

 

So we have

 

Profit =  Quantity * Price

 

Profit  =  ( 5500 - 1000x) (.75 + .50x)

 

C   If they increase the price by 1.00, x = 2   and we have

 

Profit =  (5500 - 1000 (2) ) ( .75 + .50(2) ) =

 

              (3500) ( 1.75)  =  $6125

 

D   Let us simplify the function as

 

Profit = 4125 - 750x + 2750x - 500x^2 =    - 500x^2 + 2000x + 4125 

 

We    have the form     Ax^2 + Bx + C

 

A = -500    B = 2000

 

The number of x increases that maximize the profit is given by

 

-B / [ 2A]  =     -2000 / [ 2 * -500] =  2000 / 1000 =   2  increases

 

 

 

E    So...a  $ 1.00 increase maximizes the profit...and we have  seen that this profit is $6175

 

 

Here's a graph to show this : https://www.desmos.com/calculator/lhabxwm2yz

 

 

cool cool cool

CPhill  Nov 28, 2018

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