Question

Cost Function is c(x) = 2x+5 and the revenue function is R(x) = 2x - 2x^2 where x is the number of units (in thousands) produced and sold and R and C are measured in millions of dollars.
Find:
1. Marginal Revenue
2. Marginal Cost
3. Break-even points
4. number of x for which marginal revenue equals marginal costs.

Answer 1

1) Marginal revenue is the derivative of the revenue function, so take the derivative of R(x) and evaluate it at x

2) Marginal cost is the derivative of the cost function, so take the derivative and evaluate it at x

3) For break even set your cost formula equal to your revenue formula- because they should equal each other if you "break-even"

Answer 2

What about this Solution....I am not sure people...can any one check,
a) R(x)/x = 12 - 4x
b) C(x)/x = 2
c) we want R(x) = C(x)
2x + 5 = 12x - 2x^2
12x - 2x^2-2x+5
2x^2-10x+5=0
4x-10
x = (5/2) +/- sqrt(60)/4
x = (5/2) +/- sqrt(15)/2
d) we want 12 - 2x > 2 + (5/x)
multiply by x:
12x - 2x^2 > 2x + 5
2x^2 - 10x + 5 < 0
ie ((5/2) - sqrt(15)/2 ) < x < ((5/2) + sqrt(15)/2)

Answer 3

Yes