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A company’s manager estimated that the cost CC, in dollars, of producing nn items is C=7n+350C = 7n + 350. The company sells each item for $12\$12. The company makes a profit when the total income from selling a quantity of items is greater than the total cost of producing that quantity of items. Which of the following inequalities gives all possible values of nn for which the manager estimates that the company will make a profit?\newlineA) n < 70\newlineB) n < 84\newlineC) n > 70\newlineD) n > 84

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Q. A company’s manager estimated that the cost CC, in dollars, of producing nn items is C=7n+350C = 7n + 350. The company sells each item for $12\$12. The company makes a profit when the total income from selling a quantity of items is greater than the total cost of producing that quantity of items. Which of the following inequalities gives all possible values of nn for which the manager estimates that the company will make a profit?\newlineA) n<70n < 70\newlineB) n<84n < 84\newlineC) n>70n > 70\newlineD) n>84n > 84
  1. Calculate Total Income: Calculate the total income from selling nn items at $12\$12 each: Income=12n\text{Income} = 12n.
  2. Set Up Inequality: Set up the inequality for profit, where total income is greater than total cost: 12n > 7n + 350.
  3. Simplify Inequality: Simplify the inequality by subtracting 7n7n from both sides: 5n > 350.
  4. Solve for n: Solve for n by dividing both sides by 55: n > 70.

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