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Section 4.14 : Business Applications
3. The production costs, in dollars, per day of producing \(x\) widgets is given by,
\[C\left( x \right) = 1750 + 6x - 0.04{x^2} + 0.0003{x^3}\]What is the marginal cost when \(x = 175\) and \(x = 300\)? What do your answers tell you about the production costs?
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Start SolutionFrom the notes in this section we know that the marginal cost is simply the derivative of the cost function so let’s start with that.
\[C'\left( x \right) = 6 - 0.08x + 0.0009{x^2}\] Show Step 2The marginal costs for each value of \(x\) is then,
\[\require{bbox} \bbox[2pt,border:1px solid black]{{C'\left( {175} \right) = 19.5625\hspace{0.75in}C'\left( {300} \right) = 63}}\] Show Step 3From these computations we can see that is will cost approximately $19.56 to produce the 176th widget and approximately $63 to produce the 301st widget.