Solve the problem.Marcus Tool and Die Company produces a specialized milling tool designed specifically for machining ceramic components. Each milling tool sells for $4, so the company's revenue in dollars for x units sold is R(x) = 4x. The company's cost in dollars to produce x tools can be modeled as C(x) = 299 + 30x5/8. Use Newton's method to find the break-even point for the company (that is, find x such that C(x) = R(x)). Use x = 370 as your initial guess and show all your work.

Question

What will be an ideal response?

Answer 1

Find the root of f(x) = C(x) - R(x) = 299 + 30x^5/8 - 4x.

f'(x) = x^-3/8 - 4

x₁ = 370
x₂ = 370 -  = 370 -  = 384.04
x₃ = 384.04 -  = 384.04 -   = 383.94

The break-even point is x = 383.94 tools.