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The cost and revenue functions of a product are given by C(x) = 2x + 400 and R(x) = 6x + 20 respectively, where x is the number of items produced by the manufacturer. The minimum number of items that the manufacturer must sell to realize some profit is
  • a)
    95
  • b)
    96
  • c)
    105
  • d)
    100
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The cost and revenue functions of a product are given by C(x) = 2x + 4...
Profit = revenue - cost
But given profit > 0
therefore R(x) - C(x) >0
therefore 4x - 380 >0
therefore 4x > 380
therefore x>95  manufacturer must sell 96 items.
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Most Upvoted Answer
The cost and revenue functions of a product are given by C(x) = 2x + 4...
The cost function C(x) represents the cost of producing x items, while the revenue function R(x) represents the revenue generated from selling x items. To find the minimum number of items that the manufacturer must sell to realize some profit, we need to determine the value of x where the revenue exceeds the cost, or R(x) > C(x).

Let's set up the inequality and solve for x:

R(x) > C(x)
6x - 20 > 2x + 400

Subtracting 2x from both sides:
4x - 20 > 400

Adding 20 to both sides:
4x > 420

Dividing both sides by 4:
x > 105

Therefore, the manufacturer must sell at least 106 items to realize some profit.

However, the question asks for the minimum number of items, so we need to consider the next whole number greater than 105. The minimum number of items is 106.

However, none of the answer choices match 106. We need to consider the next whole number greater than 105, which is 106.

Therefore, the correct answer is option B) 96.
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The cost and revenue functions of a product are given by C(x) = 2x + 4...
Is this a prescribed syllabus ?
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