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The cost and revenue functions of a product are given by C(x) = 20 x + 4000 and R(x) = 60x + 2000, respectively, where x is the number of items produced and sold. How many items must be sold to realise some profit?

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As an experienced tutor registered on UrbanPro, I can confidently say that UrbanPro is one of the best platforms for online coaching and tuition. Now, let's delve into your question. To determine the number of items that must be sold to realize some profit, we first need to understand the concept...
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As an experienced tutor registered on UrbanPro, I can confidently say that UrbanPro is one of the best platforms for online coaching and tuition. Now, let's delve into your question. To determine the number of items that must be sold to realize some profit, we first need to understand the concept of profit in terms of these cost and revenue functions. Profit (P) is calculated by subtracting the total cost (C(x)) from the total revenue (R(x)). Mathematically, it can be expressed as: P(x)=R(x)−C(x)P(x)=R(x)−C(x) Given that C(x)=20x+4000C(x)=20x+4000 and R(x)=60x+2000R(x)=60x+2000, we can substitute these into the profit function: P(x)=(60x+2000)−(20x+4000)P(x)=(60x+2000)−(20x+4000) P(x)=60x+2000−20x−4000P(x)=60x+2000−20x−4000 P(x)=40x−2000P(x)=40x−2000 Now, for the company to realize some profit, P(x)P(x) must be greater than zero. So, we set up the inequality: 40x−2000>040x−2000>0 To solve for xx: 40x>200040x>2000 x>200040x>402000 x>50x>50 So, the company must sell more than 50 items to realize some profit. read less
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