help me with a word problem please.?

Question

Minimizing cost- A company uses the formula c(x)= 0.02x-3.4x+150 to model the unit cost in dollars for producing x stabilizer bars. For what number of bars is the unit cost at its minimum? What is the unit cost at that level of production?

I have no clue, someone please help me thankyou

Answer 1

c(x)= 0.02x^2 -3.4x + 150 <-- I assume you meant this
Find derivative of c(x):
c'(x) = .04x -3.4
Set derivative to 0 and solve for x:
0.4x -3.4 =0
.4x = 3.4
x = 8.5 bars for minimum cost
c(8.5) = .02(8.5)^2-3.4(8.5) + 150 = $122.55 min cost/bar

Answer 2

You need a graphing calculator to accurately solve this problem. Get one and press y= at the top row of the calc. enter the equation: 0.02x-3.4x=150 click graph and then click 2nd, then trace. select the option " Minimum" and move the tracer along the graph to pick the left of the lowest bend or point of the graph. then the right of it. the calc. should give you a point, a coordinate. the x value is the number of bars you need and the y value is the cost.

Answer 3

That formula doesn't look right.
0.02x - 3.4x + 150 = -3.38x + 150
You can combine the 0.02x and -3.4x, so the original formula is too long.

Plus, there is no minimum for finite x; the more they make, the lower the unit cost.

There should be a x^2 factor in there somewhere.

Answer 4

Is your specification of the formula correct? When simplified it is a linear function f(x)=-3.38x + 150. When there is no production (x=0), the cost is 150. As x increases, f(x) decreases. The minimum value will be at maximum allowed value of x. When x >=44 ( i.e. f(x) is negative, negative cost means profit !!!)

Usually f'(x)=0 provides you with extreme values and f"(x) at that point (negative or positive) lets you know if it is minimum or maximum.

Answer 5

To find minimums and maximums of functions you must do the following:

1) find the derivative [dc/dx for your problem]

2) set the derivative equal to zero and solve for x

3) use the value of x you find back in c(x) to find unit cost at the x production level.

4) ususally common sense will tell you if what you found is a maximum or minimum.

Good luck

Answer 6

What shapes do you get whilst you cut up the rectangular with a diagonal? Two trangles. Since we all know the area is a rectangular, that suggests all of the aspects are identical (as a consequence, if you realize one part, you realize all of the aspects). So now you could have a trangle with 2 aspects identical to 60 ft. You can now use Pythagorean's theorem: A (squared) + B(squared) = C (squared) A and B are your 2 aspects and then you definitely simply clear up for C. Good success!