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You are designing a rectangular poster to contain 72 square inch of printing with a 2 inch margin...

Question:

You are designing a rectangular poster to contain 72 square inch of printing with a 2 inch margin at the top and bottom and a 1 inch margin at each side. What overall dimensions will minimize the amount of paper used?

Optimization:

Mathematical optimization is mainly used in production, inventory control (reduce inventory), transportation of raw materials or finished goods, and scheduling. In optimization problems, first, you need to identify your objective function, i.e., quantity to be maximized or minimized, and then describe it mathematically. Plugging {eq}\frac{d}{dx} f(x)=0 {/eq}, we get the values of {eq}x {/eq} at which the required quantity either hits the least value or peak value.

Answer and Explanation: 1

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Given data:

  • {eq}A_p=\rm 72 \ in^2 {/eq} is the area of the printed paper
  • {eq}x {/eq} is the width of the printed area
  • {eq}y {/eq} is the height...

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Finding Minima & Maxima: Problems & Explanation

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Chapter 5 / Lesson 2
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One of the most important practical uses of higher mathematics is finding minima and maxima. This lesson will describe different ways to determine the maxima and minima of a function and give some real world examples.


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