The cost (in dollars) for a publisher to produce 𝑥 books is 𝐶(𝑥) = 𝑥2 − 3000𝑥 + 5000 Find the number of books that must be produced to minimize the cost.

Question

Can you help me solve this equation step by step please

Answer 1

C = x^2 -3000x +5000

rewrite in vertex form, vertex = minimum point

complete the square

x^2 -3000+ 1500^2 + 5000 - 1500^2

(x-1500)^2 + 5000 -2,250,000

(x-1500)^2 - 2,245,000

minimum x = 1500 books

minimum cost = a loss of $2,245,000