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**+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**+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

CPhill
Nov 28, 2018