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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Given that,

Cost, C(x) = 20 x + 4000

Revenue, R(x) = 60x + 2000

We know that, profit = Revenue – Cost

Now, subsitute the given data in the above formula,

Profit = R(x) – C(x)

Profit = (60x + 2000)-(20 x + 4000)

Now, simplify it:

Profit = 60x + 2000 -20x -4000

Profit = 40x – 2000

To earn some profit, 40x – 2000 > 0

⇒40x > 2000

⇒ x>2000/40

⇒ x > 50

Thus, the manufacturer should sell more than 50 items to realise some profit.

Thanks