Q.The cost and revenue function of a product are given by C(x) = 2 x + 400 and R (x) = 6 x + 20 respectively , where x is the number of items produced by the manufacturer.Then, the number of items must sell to produce to realize some profit is
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Answer:We have, profit = Revenue – Cost = (60x + 2000) – (20x + 4000) = 40x – 2000 To earn some profit, 40x – 2000 > 0 ⇒ x > 50 Hence, the manufacturer must sell more than 50 items to realise some profit. - the-cost-and-revenue-functions-of-a-product-are-given-by-c-x-20-x-4000-and-r-x-60x-2000
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We know that,
Now,
Subsitute the given data in the above formula,
Profit = R(x) – C(x)
Profit = (60x + 2000)-(20 x + 4000)
60x + 2000 -20x -4000
40x – 2000
To earn some profit,
⇒40x – 2000 > 0
⇒40x > 2000
⇒ x > 2000/40
⇒ x > 50
Thus,
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