Find and interpret R(10) and P(10)

Question

The cost, in dollars, to produce x widgets is C(x) = 5x + 20 , x > 0.

The price-demand function, in dollars per widget, is p(x) = 30 - x.

a. Find and interpret R(10), where R(x) is the revenue function.

b. Find and interpret P(10), where P(x) is the profit function.

Answer 1

Revenue is the total amount of income generated by the sale of goods.

Let assume we sold x number of widgets. Revenue will the price of each widget and number of widgets. p(x) is the price demand function.

R(x) = x(30-x)

R(10) = 10 (30-10) = 200

So, after selling 10 widgets, total amount of income generated by the sale of goods is 200 dollars.

P(x) = R(x) - C(x)

Profit function tells you how much profit did u made which can be calculated from by subtracting the cost of making products from revenue.

P(10) = R(10) - C(10)

P(10) = 200 - (5*10 +20)

P(10) = 200 - 70 = 130

So, the profit by selling 10 widgets is 130 dollars.

I hope this helps.