the table below shows possible cost and revenue equations for a manufacturer of cameras.\n| cost | 65.16n +…

Explanation:

Step1: Recall break - even condition

At break - even, cost = revenue. Let's set up equations for each pair and check if they have a non - negative solution for $n$.

Step2: Analyze pair I and III

Set $65.16n + 1500=98.75n$. Then $98.75n-65.16n = 1500$, so $33.59n=1500$, and $n=\frac{1500}{33.59}\approx44.65$ (a non - negative solution exists).

Step3: Analyze pair I and IV

Set $65.16n + 1500=56.95n$. Then $65.16n-56.95n=- 1500$, so $8.21n=-1500$, and $n =-\frac{1500}{8.21}<0$. Since the number of units $n$ (a real - world quantity) cannot be negative, this pair will never break even.

Step4: Analyze pair II and III

Set $35.79n + 6700=98.75n$. Then $98.75n-35.79n = 6700$, so $62.96n=6700$, and $n=\frac{6700}{62.96}\approx106.42$ (a non - negative solution exists).

Step5: Analyze pair II and IV

Set $35.79n + 6700=56.95n$. Then $56.95n-35.79n = 6700$, so $21.16n=6700$, and $n=\frac{6700}{21.16}\approx316.63$ (a non - negative solution exists).

Answer:

b. I and IV