SOLUTION: Please help me solve this problem. I'm not sure if the steps I used are correct so I would need the steps so I can understand it better. I think the answer is 320< x <480, but I'm

Question 230221: Please help me solve this problem. I'm not sure if the steps I used are correct so I would need the steps so I can understand it better. I think the answer is 320< x <480, but I'm not positive. Thanks in advance for your help. The problem is the following: 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?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

You have exactly the correct answer IF you presume that the word "between" as used in "between $525,000 and $781,000" means (or at least implies) that the costs cannot actually equal either $525K or $781K. If you allow inclusion of the endpoints of the given cost range, then your manufactured items range must be:

I presume that the steps of procedure you used were to set the cost function equal to each of the cost range end points (expressed in $100s) and then solve for

, thus:

and

The question about the inclusion of the endpoints comes up because the solutions to the above equations are both integer values.

John

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