Assume that the mathematical model C(x) = 16x + 130 represents the cost C, in hundreds of dollars, for a certain manufacturer to produce x items. How many items x can be manufactured while keeping costs between $525,000 and $781,000? Thanks for the help in advance! :)
Ohhh ,i'm on this chapter right now. Okay, is there a value for x? if not, make an x and y table chart, i normally start with zero which i highly recomend you doing.
okay once you decide on what you are going to set x as, fill it in like this:
Example- C(0)= 16(0)+130
C(0)= 0 +130
C(0)= 130
You try it now.
if you have any questions, i'm right here waiting to answer them.
5,250=16x+130
16x=5,250-130
16x=5,120
x=5,120/16
x=320
7,810=16x+130
16x=7,810-130
16x=7,680
x=7,680/16
x=480
This is what I came up with is this correct?
I got the same thing. I hope it's right
what did you set x as?
oh, i get it , you're trying to do the linear equation type of way, he's talking about linear functions, you know... f(x)=mx+b
So is {x| 320 < x <480 correct?
Where did this question come from?
To find the range of items that can be manufactured while keeping costs between $525,000 and $781,000, we need to set up an inequality using the given mathematical model: C(x) = 16x + 130.
First, let's convert the cost limits from dollars to hundreds of dollars, since the model is in hundreds of dollars:
Lower cost limit: $525,000 / 100 = 5250 hundreds of dollars
Upper cost limit: $781,000 / 100 = 7810 hundreds of dollars
Now, we can write the inequality:
5250 ≤ 16x + 130 ≤ 7810
Subtract 130 from all parts of the inequality:
5120 ≤ 16x ≤ 7680
Divide all parts by 16 to solve for x:
320 ≤ x ≤ 480
Therefore, the range of items that can be manufactured while keeping costs between $525,000 and $781,000 is 320 ≤ x ≤ 480.