Thursday

May 5, 2016
Posted by **Yvette** on Wednesday, July 25, 2007 at 10:06am.

Here's the problem:

The PTO of Parksville Elementary School is having a Bazaar and all of the classes are expected to contribute to this fun and exciting event. The third grade teachers , along with some dedicated parents(e.g. YOU!), decide to sell cotton candy. A little research shows you can get the machine for $40, cleaning supplies will cost $10. The sugar/cone combo packages that cost $10 each will serve 100. The committee thinks they could probably sell 180 of these puffy globs of goodness, so they order two packages. (Note: You can get a refund for unopened packages--so only open them as needed). One of the parents asks: If we sell the cotton candy $1.50 each, how many servings must be sold to break even? You have volunteered to create the equations and graph the cost analysis chart so you will be able to answer that question, as well as the following questions:

a. What are the Cost equations? Graph these equations.

b. What is the Revenue equation? Graph this equation.

c. Where do these two lines cross? (Where is the Break-Even point?)

d. Profit equals Revenue minus Costs (P=R-C). What are the Profit equations?

e. How much profit will be made if 99 cones are sold?

f. What's the profit if 102 cones are sold? Do you always make more by selling more?

g. How much profit will be made if 150 servings are sold?

h. If the committee wants to make $300, how many cones must be sold? Can you do it?

i. How much would you have to sell each cone for to make a profit of $300 w/o getting extra supplies?

They sure make "word problems" harder by putting in so many words. Yours reads like a Jane Austen novel.

I suggest you let x be the number of cones sold.

a. For the cost equation, if you sell 100 or less, the cost is

C(x) = 50 + 10 = 60

If you sell 101 to 200, the cost is

C = 70 (since new box of 100 must be openied)

If you sell 201 to 300, the cost is C= 80, etc.

The cost function looks like a flight of stairs. You draw it.

b. The Revenue equation is

R = 1.5 X ($1.50 per cone)

c. You can make break even by selling less than 101.

Just set R = 1.5 X = 60 and solve for X

d. I have already told you what C anr r look like. You plot R

e. For 99 cones,

P = 99 x 1.5 - 60 = $88.50

f. For 102 cones,

P = 102 x 1.5 - 70 = $83.00

Use similar logic for g and h

i. I assume that "without getting extra supplies" means selling 200 cones. Allowing for a differnt selling price P, the profit (if you sell them all)would be

P*200 - 70 = 300

200 P = 370

P = $1.85