A company makes jackets. If x represents the number of jackets produced, the total cost function for producing x jackets is C(x) = 0.43x^2+18.3x+15.6 and the demand function is p = -0.02x+129 , consider the following two questions:

a) What is the marginal profit function?

b) Suppose the company is making and selling 6 jackets per day at the time the 100th jacket is produced, what is the rate of change per day of its total profit?

i) What kind of problem is this and how do you know?

ii) Solve the problem.

Question

A company makes jackets. If x represents the number of jackets produced, the total cost function for producing x jackets is C(x) = 0.43x^2+18.3x+15.6 and the demand function is p = -0.02x+129 , consider the following two questions:

a) What is the marginal profit function?


b) Suppose the company is making and selling 6 jackets per day at the time the 100th jacket is produced, what is the rate of change per day of its total profit?

i) What kind of problem is this and how do you know?

ii) Solve the problem.

anonymous · Answer

revenue = p * x = (-0.02x+129)x
profit = (-0.02x+129)x - 0.43x^2 + 18.3x + 15.6
marginal profit function = derivative of profit function