C(x)300x+2000 R(x)=400x

Answer 1

This looks like a microeconomics problem, where R(x) = Total Revenue, C(x)= Total Cost = Variable Cost + Fixed Cost. So Fixed cost = 2000. Variable Cost = 300x

The usual problems are find the break even point, or find the profit maximizing out put level.

Set R(x)=C(x) and solve for x to find the break even point. 300x+2000=400x

100x=2000, so x = 20. When you produce 20 units, you break even or profit = 0. Produce less than 20, x<20 and you suffer a loss, or negative profit. Produce more than 20, x>20 and you gain a profit.

Profit is R-C = 400x-300x+2000 = 100x +2000

The profit maximizing level of output is infinite. The more you make & sell, the greater the profit. That's not realistic, as it assumes price is constant. IF you produce too much, it saturates the market and price comesdown. 400x as R(x) falsely assumes you'll always get 400 per unit, regardless how much you sell. C(x)=300x+2000 also falsely assumes 2000 for fixed cost is enough to support an endlessly larger output. But the problem may make sense for some limited range of output. There might be some other information missing from the problem that could make the profit maximizing output unique and finite.