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Think Break #4

Think Break #4. Find X to Maximize: p = 10(30 + 5X – 0.4X 2 ) – 2X – 18 1) What X satisfies the FOC? 2) Does this X satisfy the SOC for a maximum?. Think Break #4: Answer. Find X to Maximize: p = 10(30 + 5X – 0.4X 2 ) – 2X – 18 1) FOC f’(X) = 0, solve for X 10(5 – 0.8X) – 2 = 0

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Think Break #4

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  1. Think Break #4 Find X to Maximize: p = 10(30 + 5X – 0.4X2) – 2X – 18 1) What X satisfies the FOC? 2) Does this X satisfy the SOC for a maximum?

  2. Think Break #4: Answer Find X to Maximize: p = 10(30 + 5X – 0.4X2) – 2X – 18 1) FOC f’(X) = 0, solve for X 10(5 – 0.8X) – 2 = 0 50 – 8X = 2 → 48 = 8X X = 6 2) SOC: f’’(X) < 0: f’’(X) = – 8 < 0 X = 6 is a maximum

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