An official can embezzle funds from a project worth 50 million Naira. The probability $p$ of being caught depends on the amount embezzled $x$ (in million Naira) as follows: $ p = \begin{cases} 0.05, & x\le 5,\[2mm] 0.05+0.02\,(x-5), & x5. \end{cases} $ If caught, the official must return the embezzled amount and pay a fine equal to 150\% of the embezzled amount. The official seeks to maximise the expected net gain (embezzled amount minus expected penalty). Determine the amount $x$ that maximises the expected net gain and compute that maximum expected net gain (in million Naira), rounded to two decimal places.

Question

An official can embezzle funds from a project worth 50 million Naira. The probability $p$ of being caught depends on the amount embezzled $x$ (in million Naira) as follows: $ p = \begin{cases} 0.05, & x\le 5,\[2mm] 0.05+0.02\,(x-5), & x>5. \end{cases} $ If caught, the official must return the embezzled amount and pay a fine equal to 150\% of the embezzled amount. The official seeks to maximise the expected net gain (embezzled amount minus expected penalty). Determine the amount $x$ that maximises the expected net gain and compute that maximum expected net gain (in million Naira), rounded to two decimal places.

Accepted Answer

Embezzle 11.25 million Naira; maximum expected net gain ≈ 6.33 million Naira

Neco 2024 Civic Education Question 29

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