The cost, in dollars, to produce xx designer dog leashes is C(x)=5x+5, and the price-demand function, in dollars per leash, is p(x)=71−3x

Question

The cost, in dollars, to produce xx designer dog leashes is C(x)=5x+5, and the price-demand function, in dollars per leash, is p(x)=71−3x

Find the profit function. 

P(x)=  

---Find the number of leashes which need to be sold to maximize the profit.

----Find the maximum profit.

----Find the price to charge per leash to maximize profit. 

 ----What would be the best reasons to either pay or not pay that much for a leash?

Answer 1

the Demand function is D(x) = 71-3x

The revenue function is

R(x) = x * D(x)

= x ( 71 - 3x)

= 71x - 3x^2

The profit function is:

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

71x - 3x^2 - (5x+5)

=71x - 3x^2 - 5x - 5

= -3x^2 + 66x - 5

Maximizing:

0=dP/dx = -6x+66

x = 11