Help with Fundraising question - Which item should the school sell?

Question

Your school of 1000 students wants to purchase a new awning for the patio, at a cost of $3,950 including tax and shipping.

You have 2 options for raising the money:

Option 1: Sell frozen juice pops four times a week at a profit of $0.17 each.

Option 2: Sell chips twice a week at a profit of $0.42 per bag.

Everyone likes frozen juice pops, but only 80% of the students like chips.

Assume if someone likes something, they will buy it every time it is offered for sale.

A. How many weeks will it take you to meet your goal of $3,950?

B. How can you shorten the time to reach your goal?

C. What are some factors that will influence your choice of what to

sell?

Answer 1

Hi, Christy.

This problems looks at a few different things. Let's look at Option 1 first.

Option One: If the students sell juice pops 4 times a week, they will make a profit of $0.17/ pop per person.

Also, it says that every student likes juice pops and that, if a student likes the product, you

should assume that they will buy the product each time it is offered for sale. Since there are

1,000 students, you should assume that each day the pops are sold, that all 1,000 students

will buy one. Therefore, the commission would be :

1,000 x $0.17 = $170 a day times 4 days a week

= $170 x 4 = $680 / week

Option Two: If the students sell chips twice a week, they will make a profit of $0.42 / bag. However, since

only 80% of the students like chips, you should assume that only 800 students (80% of 1,000)

will buy the chips each day they are sold. Therefore, the commission would be:

800 x $0.42 = $336.00 a day, 2 days a week

= $336 x 2 = $672 / week

As you can see, the juice pops bring in a slightly greater profit per week.

To find out how many weeks it will take to meet your goal, you simply divide $3950 by the profit per week.

For juice pops, you would have: $3950 ÷ 680 = 5.8 weeks... rounded to 6 weeks.

For the chips, you would have: $3950 ÷ $672 = 5.9 weeks....also rounded to 6 weeks.

For the rest of the question, you need to decide what could help shorten the time to reach your goal and also look at some of the factors that could influence what you sell. Consider, for instance, that the juice pops would need to be kept frozen and how that might make them more time-consuming to sell. Also consider the difference in the number of hours required to sell 4 times a week versus 2 times a week.

Can you come up with some other factors which make one item more favorable than the other?

I hope this helps.

Answer 2

Option 1: $3950 ≤ 1000(4)($0.17)w

Option 2: $3950 ≤ 80(2)($0.42)w

Can you solve for w and answer?