The cost in millions of dollars for a company to manufacture

The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x) = 5x^2 - 300x + 6000 Find the number of automobiles that must be produced to minimize the cost. Include correct units in your answer. Find the minimum cost. Include correct units in your answer.

Solution

C(x) = 5x^2 - 300x +6000

a) Its a quadratic function .Quadratic function, minimum /max . would

occur at vertex given by x = -b/2a

x = -(-300)/10 =30 thousand automibiles . of must be produced

b)Minimum cost : C(30) = 5(30)^2 - 300*30 +6000 = 1500 million dollars