A manufacturer determines that the profit derived from selling x units of a certain item is given
by: P = − 2x^2 +800x Find the marginal profit for a production of 20 units.
Also,
The demand function for a particular commodity is given by: p = 400− 4x . Find the
marginal revenue when x = 20.
These are arithmetic questions
Just plug the given values into the equations.
P = -2(20^2) + 800(2) = .....
To find the marginal profit and marginal revenue, we need to take the derivative of the profit and revenue functions, respectively, with respect to the number of units (x) produced or sold.
1. Marginal Profit:
The profit function is given by P = -2x^2 + 800x. To find the marginal profit, we take the derivative of P with respect to x.
dP/dx = d/dx (-2x^2 + 800x)
= -4x + 800
Now, substitute x = 20 into the expression above to find the marginal profit for a production of 20 units:
marginal profit = -4(20) + 800
= -80 + 800
= 720
Therefore, the marginal profit for a production of 20 units is 720.
2. Marginal Revenue:
The revenue function is given by R = p * x, where p is the price per unit and x is the number of units sold. In this case, the demand function is given by p = 400 - 4x.
To find the marginal revenue, we take the derivative of R with respect to x:
dR/dx = d/dx (p * x)
= d/dx [(400 - 4x) * x]
= (400 - 4x) + (-4) * x
= 400 - 4x - 4x
= 400 - 8x
Now, substitute x = 20 into the expression above to find the marginal revenue when x = 20:
marginal revenue = 400 - 8(20)
= 400 - 160
= 240
Therefore, the marginal revenue when x = 20 is 240.