An Aircraft Manufacturer Wants to Determine the Best Selling Price $$m ( x ) = 1,600 x + 40 x ^ { 4 / 5 } + 0.15 x ^ { 2 }$$

Short Answer

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 700 million dollars. The additional cost of manufacturing each plane can be modeled by the function
$$m ( x ) = 1,600 x + 40 x ^ { 4 / 5 } + 0.15 x ^ { 2 }$$
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
$$x ( p ) = 390 - 5.8 p$$
Find the cost function.