I need help with this math problem.?

Question

The manufactor will charge you a time fee of $1000 to produce the glasses with the Laurel Highlands Mustang printed on them. The manufacturer will sell each glass $1.15. Your torla on one glass would be $1001.15($1000+$1.15), for two glasses your cost would be $1002.30 ($1000+$2.30), and so on.

Your planning to sell them for $ 4.95 Each.

Using the above information, you need to complete the following tasks.

1)Generate two linear equations, one that will accurately calculate your total cost for any number of glasses sold, and one that will accurately calculate your total revenue(money you get from the sales).

2) Determine the number of glasses you need to sell to break even(when your revenue equals your cost). You will do this by solving the system of equations you created in step 1.

3.Determine the number of glasses you need to sell to make $4000(when your revenue is $4000 greater then your cost.) A simple change in the equations from step 2 will accomplish this.

Answer 1

cost is y = 1.15x + 1000
revenue is y = 4.95x
where x is the number of glasses

break-even is when
1.15x + 1000 = 4.95x
solve and get x = 263.16 so you must say
264 glasses

3rd part"
[4.95x] - [1.15x + 1000] = 4000
solve this
get x = 1315.79 so you must say 1316 glasses

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Answer 2

let x = the number of glasses produced:

the total cost is 1000 + 1.15x

let y = the number of glasses sold:

the total revenue is 4.95y

We want to know the quantity that will make these two even:

1000 + 1.15x = 4.95x
1000 = 3.8x
x = 263.15789

If you made and sold 263, the cost would be:

1000 + 263*1.15 = 1302.45

revenue would be:

263 * 4.95 = 1301.85


Now, how many would we need to sell to make a profit of 4000? To calculate this, we know revenue needs to exceed cost by 4000, so:

1000 + 1.15x + 4000 = 4.95x
5000 = 3.8x
x = 1315.789 (we'll say 1316)

If we made 1316, our cost would be:

1000 + 1316(1.15) = 1513.40

Revenue would be:

1316(4.95) = 6514.20

Total profit is:

6514.20 - 1513.40 = 4000.80

Hope this helps! :)

Answer 3

Cost = $1000 + N ($1.15)
Revenue = N ( $4.95)

Profit = Revenue - Cost = 4.95 N - 1.15 N - 1000
For Break Even, 0 = 3.80 N -1000 or N = 263.15 meaning you need to sell N = 264 units

For a profit of $4000, 4000 = 3.80N - 1000 or N = 1315.78 meaning you need to sell N = 1316 units.

An equivalent way of looking at such problems is to consider the "contribution margin" which is 4.95 - 1.15 = 3.80. Whatever the fixed amount is that you wish to achieve, dividing it by the contribution margin yields the number of units you must sell.

Answer 4

Equations for revenue and cost:
Cost=1000+1.15N
Revenue = 4.95N

To make cost equal revenue set the equations equal to each other and solve for N:

1000 + 1.15N=4.95N
1000 =3.8N
N=263.158 so you need to sell 264 glasses to get you cost back

to make 4000 profit subtract cost from revenue and set equal to 4000:

4.95N-1000-1.15N=4000
3.8N-1000=4000
3.8N=5000
N=1315.789 so you must sell 1316 glasses to make 4000 profit.