Question

The total cost function for a product is

𝐶(𝑥) = 30𝑥 + 1200 and the total revenue is 

𝑅(𝑥) = 38𝑥 where 𝑥 is the number of units produced 

And sold. 

a) Find marginal cost. 

b) Find profit function. 

c) Find the number of units that gives break even. 

d) Find marginal profit and explain what it means. 

Answer 1

a)

$$MC(x) =dC/dx=30$$

b)

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

$$P(x)=38x-(30x+1200)$$

$$(x)=8x-1200$$

c)

$$P(x)=0=>8x-1200=0$$

$$x=150$$

d)

$$MP(x)=dP/dx=8$$

The profit obtained by producing and selling one additional item is 8.