Solve the Problem $\$ 4$ , So the Company's Revenue in Dollars For

question 297

Essay

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 $R ( x ) = 4 x$ . The company's cost in dollars to produce $x$ tools can be modeled as $C ( x ) = 304 + 30 x ^ { 5 / 8 }$ . 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.

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Definitions:

Unpredictable Demand

Variability in customer demand patterns that cannot be accurately forecasted, posing challenges for inventory management and planning.

Not Positively Correlated

Refers to a statistical relationship between two variables where one variable does not necessarily increase as the other increases or decreases as the other decreases.

Multiple Smaller Orders

Refers to the strategy of breaking down large orders for goods or services into smaller ones, often to manage risk, improve cash flow, or respond more flexibly to market demand.

Match Supply

the process of adjusting production levels, inventory, or supply chain capacities to meet the current or forecasted demand effectively.