Question

for a certain commodity the demand function is given by D=100(10-p)and the supply function is S=75(p-3)find the equilibrium price and quantity
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Answer 1

Step-by-step explanation:

The profit function is given by

P(x)=xp(x)−C(x)

=x(10−0.001x)−(50+5x)

=10x−0.001x

2

−50−5x

=5x−0.001x

2

−50

Take the derivative of P(x) :

P

′

(x)=5−0.002x

So, the critical point is

x=2500

Since, the second derivative of P(x) is negative, x=2500 is a point of maximum.

Hence, the company has the largest profit when x=2500.