The cost and revenue functions of a product are given by `C(x) = 20x +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?

The cost and revenue functions of a product are given by `C(x) = 20x +

1.	The cost and revenue functions of a product are given by `C(x) = 20x +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?
Answer» Let the required number of items sold be x and let P(x) be the profit function, Then, profit function = (revenue function) - (cost function) `rArr P(x)=(60x+2000)-(20x+4000)` `rArr P(x) = 40x -2000`. For some profit, we have `P(x)gt 0`. `therefore 40x-2000 gt 0` `rArr 40x gt 2000` `rArr x gt 50` Hence, the manufacturer must sell more than 50 items ot realise some profit.