Question

Let’s consider this problem:

I want to start a lemonade stand and determine how much lemonade I need to sell to break even each day.

If I know I spend $5 on supplies and sell the lemonade at $0.50 per glass determine the number of glasses I must sell to break even. After you find the number of glasses tell me what the x-intercept, y-intercept, and slope represent in the function you determined.

Your answer should include:

1. Number of glasses
2. x-intercept
3. y-intercept
4. slope

Answer 1

Let Q be the number of glasses of lemonades that I sell. I sell each glass of lemonade for $0.50. The revenue (money) that I make by selling Q glasses of lemonade is

Revenue = 0.5*Q

I spend $5 on the supplies. This I spend irrespective of the number of glasses of lemonade I sell. Hence the cost of lemonade is

Cost = 5

The profit that I make by selling Q glasses of lemonade is

I break even when when the money that I make from selling is equal to the cost of the supplies. That is I break even when the profit is zero.

Hence

That is if I sell 10 glasses of lemonade each at $0.5, I make $5 in revenue and hence I break even as it is equal to the money that I spent on the supplies.

ans: Number of glasses that I must sell to break even is 10

The profit function is

Let us assume that Profit is y axis and Q (the quantity) is along the x-axis.

The value of profit for different quantity is given below

Quantity (Q)	Profit ($)
0	-5
1	-4.5
2	-4
3	-3.5
4	-3
5	-2.5
6	-2
7	-1.5
8	-1
9	-0.5
10	0
11	0.5
12	1
13	1.5
14	2
15	2.5

If we plot this we get

The y intercept is obtained when we set Q=0. That is

Ans: The y-intercept is -5. This means that the profit is -$5 when the quantity is 0. It means that if I sell 0 glasses of lemonade I make a loss of $5.

The x-intercept is the value of Q when the Profit is 0. This is the break even quantity that we have already calculated.

ans: The value of x-intercept is 10. It indicates the number of glasses I must sell to break even.

Finally slope is the coefficient which is used to multiply the quantity (x-axis values) in the function.

ans: The value of the slope is 0.5. It indicates that if the number of glasses of lemonade sold increases by 1, the profit increase by $0.5.