A company’s manager estimated that the cost C, in dollars, of producing n items is C=7n+350. The company sells each item for $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 n for which the manager estimates that the company will make a profit?A) n < 70B) n < 84C) n > 70D) n > 84
Q. A company’s manager estimated that the cost C, in dollars, of producing n items is C=7n+350. The company sells each item for $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 n for which the manager estimates that the company will make a profit?A) n<70B) n<84C) n>70D) n>84
Calculate Total Income: Calculate the total income from selling n items at $12 each: Income=12n.
Set Up Inequality: Set up the inequality for profit, where total income is greater than total cost: 12n > 7n + 350.
Simplify Inequality: Simplify the inequality by subtracting 7n from both sides: 5n > 350.
Solve for n: Solve for n by dividing both sides by 5: n > 70.
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