Think Break #5

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?

Think Break #5: Answer

Find X to Maximize: p = 10(30 + 5X – 0.4X2) – 2X – 18

1) FOC f’(X) = 0, solve for X10(5 – 0.8X) – 2 = 050 – 8X = 2→ 48 = 8XX = 6

2) SOC: f’’(X) < 0: f’’(X) = – 8 < 0X = 6 is a maximum