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Asked by Geeta Last Modified
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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.
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