Given that price per unit 2300D20 where D is the annual de

Given that price per unit ($) = 2,300-D20, where D is the annual demand (units) and total cost per year can be approximated by $2,000+3D. a. What level of annual demand maximizes profit? How do you know you haven\'t 2. minimized profit? What is the maximum profit (S) per year? b.

Solution

As per principle, profit is maximized when Marginal cost = Marginal Revenue, By going to this fact,

Given, P = 2300 – D/20, where P is price and D is demand

So Total Revenue = PxD = 2300D-D^2/20

And Marginal Revenue = 2300 – D/10

Given Total Cost = 2000 + 3D^2

Marginal Cost = 6D

MC = MR

6D = 2300-D/10

6D + D/10 = 2300 => 61D/10 = 2300

61D = 23000 => D = 377.05, so At the demand level of 377 units Profit will be maximized.

Part b: Maximum profit will be Total Revenue less Total cost

Total Revenue = 2300 x 377 – 377^2/20 = $859,993.55

Total Cost = 2000+ 3 x 377^2 = $428,387

Maximized Profit = 859,993.55 – 428,387 = $431,606.55