Question

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

Answer 1

The company must sell at least 50 items in order to realize some profit.

Step-by-step explanation:

In order to realize some profit, the revenue must exceed the cost. We can calculate the break-even point by setting the cost function equal to the revenue function and solving for x:

C(x) = R(x)

By substituting the given cost and revenue functions, we have:

20x + 4000 = 60x + 2000

Simplifying the equation, we get:

40x = 2000

Solving for x, we find that:

x = 50

Therefore, in order to realize some profit, the company must sell at least 50 items.