My brain is dead, can someone help me?

Question

An inventor of a new product believes that the cost of producing the product is given by the function, C(x)=1.75x + 7000.

If that inventor charges $4.00 per unit, then her profit for producing and selling x units is given by the function, P(x)=2.25x - 7000
(a) profit if she sells 2000 units
(b) profit if she sells 5000 units
(c) Break even point for sales

Answer 1

The two equations you are given are just two different ways to express the information. The way this is set up assumes that the inventor will be able to sell every item that is produced, so both her production and sales are represented by "x".

To see that the two equations are really giving you the same information, notice that:

Sales - cost =profit. Sales would be 4.00x.
4.00x-(1.75x+7000)=2.25x-7000

The break even point is when your profit is zero, so you are neither losing nor gaining money.
P(x)=0. This point would be called the y-intercept if you were drawing a graph.

Also, if you look at your two equations, you can see that they are written in the form, y=mx+b, so you could graph the equation, and read the points off the graph, where:

(a) x=2000
(b) x=5000
(c) the value of x when y=0.

Or if you feel more comfortable with the algebra, just use your equations.

The best way is to find the answer by two different ways, and see if they agree. For a quick check, you can just compare the answers and see if they make sense.

Just by noticing that the slope is positive, you can already tell that the profit for 5000 units should be greater than for 2000 units.

Little ways to check your work are especially helpful during an exam.

Answer 2

(a) 2.25*2000-7000 = -2500
i.e a loss of $ 2500

(b) 2.25*5000-7000 = 4250
i.e a profit of $ 5500

(c) break even points implies 2.25x-7000 ≥ 0
x ≥ 7000/2.25 = 3111 1/9
Since x must be integral, x=3112 products

Answer 3

Profit is going to be P(x) so substitute in for x.

P(2000) = 2.25(2000)-7000 = 1500

P(5000) = 2.25(5000) - 7000 = 4250

You will break even when your profit is zero. So P(x) is going to equal to zero.

2.25x - 7000 = 0

2.25x = 7000

x = 7000/2.25

Answer 4

(a) 2.25*2000-7000 = -2500
i.e a loss of $ 2500

(b) 2.25*5000-7000 = 5500
i.e a profit of $ 5500

(c) break even points mean no profit no loss
i.e 2.25x-7000=0
x=7000/2.25 = 3111 products

Answer 5

Just plug in each number they give you. For part a, make x=2000, for part b make x=5000, and for part c make the profit equal zero (that is, set the whole equation equal to zero and solve for x. I don't know if you wanted the actual answer or not, so I assumed you werent trying to cheat. Just grab a calculator and plug the numbers in.

Answer 6

i> loss of 2500 $
ii> profit of 4250 $
iii> break even point is 7000/2.25=3111.11=3111(approx.)

Answer 7

how r u talking/typing if youre brain is dead??? man some people

Answer 8

i'm sorry about your brain. Too bad brain cells aren't able to regenerate.

Answer 9

The (b) man

Answer 10

is ur brain really dead?...or is it a joke?!!!