Question

ok I need a real math wiz
Scenario: Suppose your business makes high-grade PDAs, personal digital assistants. It costs you $80,000 a month for fixed costs, such as rent, employee salaries, and other essential items. Also, it costs $300 to make each PDA, called a unit. If you are able to sell each unit for $500, how many PDAs do you need to sell to break even?

Answer 1

It just needs knowledge of basic algebra. Have you identified the variable?

Answer 2

it also says Step 1: Set up the variables. Let x = the number of units
y = the cost/income (expense/revenue) in dollars

Answer 3

step 2
Cost Equation:
total cost = fixed cost + (cost to make each unit) · (# of units)
y =

Income Equation:
total income =
y =

Answer 4

step 3
Step 3: Solve the system of equations using substitution.

Answer 5

step 4
Step 4: State the break-even point.

Answer 6

ok so first for step 1 I set up the variables

Answer 7

Let x = the number of units
y = the cost/income (expense/revenue) in dollars

Answer 8

x=?
y=300/500(80,000/x)

Answer 9

The variables have already been set up. But you dont need variable y, revenue in dollars. Just x is sufficient

Answer 10

is that right?

Answer 11

but it says to set y up

Answer 12

It can be solved more simply using just one variable.

Answer 13

ok

Answer 14

so x=?

Answer 15

number of PDAs

Answer 16

which I dont know

Answer 17

Which is the only thing you dont know in this equation and have to find out

Answer 18

oooooo wait do I divide 80000/300?

Answer 19

I dont think so. It is just the overhead cost. You have to keep it as it is.

Answer 20

wait im confused

Answer 21

so x=?

Answer 22

x is number of PDAs you have to make to balance the overhead cost and the cost of making PDAs.

Answer 23

ok so x=80,000+300?

Answer 24

No, x will be present on both sides of the equation, which has expense amount on one side and revenue amount on the other side.

Answer 25

so x=80,000+(300*x)?

Answer 26

Yes that will be the left side of your equation.

Answer 27

ok now what?

Answer 28

Now write the right side of your equation. What will the total revenue be?

Answer 29

x*y?

Answer 30

y ?

Answer 31

the total would be x* 80,000 * (300*x)

Answer 32

i think

Answer 33

The total EXPENSE (cost of making the PDAs) will be 80000 + 300*x. I hope you understand this.

Answer 34

I thought that was the left side of the equation

Answer 35

Yes it was. Right side of the equation will be
Money from one PDA * number of PDAs

Answer 36

so
x*80,00*(300*x)=500*x
is my final equation?

Answer 37

or no wait i would have 2 equation right?
x*80,000*(300*x)
and
500*x

Answer 38

Not x*80,00*(300*x) , 80,000 + 300*x
80000 is not required for 1 pda, it is the total amount for all pdas

Answer 39

o whoops

Answer 40

so 80,000+300*x
and 500*x
are my equations?

Answer 41

Your one equation in one variable is
80,000 + 300*x = 500*x
You can solve for x easily

Answer 42

An equation always has two sides

Answer 43

80,000 + 300*x = 500*x
200*x=80,000
x=80,000/200
x=400

Answer 44

right?

Answer 45

Yes. Congrats! So now you are a maths whiz.

Answer 46

haha thatnks but how do I find the break even point?

Answer 47

The break even point is the number of PDAs you need to sell to make expense and revenue even. So it is 400, the answer you got.

Answer 48

o

Answer 49

but then it says The following graph represents the above information about your hypothetical business. Label the y-axis with appropriate units and the break-even point with coordinates. Also, write on each line either "cost" or "revenue" to indicate what each represents.

Answer 50

so does it want me to graph it?

Answer 51

Here you have to variable y.

Answer 52

ok

Answer 53

In the graph the x axis will be number of pdas and y axis will be expense/revenue.

Answer 54

so would it look like

Answer 55

wait they want coordinates? where do I put them?