Question

An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial cost of designing the airplane and setting up the factories in which to build it will be 500 million dollars. The additional cost of manufacturing each plane can be modeled by the function:

Answer 1

Answer:

The cost function is simply the initial cost plus the manufacturing cost.

C(x)=500+20x-5x^3/4+0.01x^2

The demand function was given to us.

p(x)=320-7,7x

The revenue function is simply x multiplied by the demand function.

R(x)=xp(x)=320x-7.7x^2

We find that when 20 planes are produced, that profit is currently maximized

We know that to maximize profit, marginal revenue must equal marginal cost.

C'(x)=20-15/4x^-1/4+0.02x

R'(x)=320-15.4x

x=19,57

We find that when 20 planes are produced, that profit is currently maximized.

Step-by-step explanation:

An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial cost of designing the airplane and setting up the factories in which to build it will be 500 million dollars. The additional cost of manufacturing each plane can be modeled by the function: , where x is the number of aircraft produced and m is the manufacturing cost, in millions of dollars. The company estimates that if it charges a price p (in millions of dollars) for each plane, it will be able to sell  planes.

(a) Find the cost, demand, and revenue functions.

(b) Find th eproduction level and the associated selling price of the aircraft that maximizes profit.