Please help me Question The Orange County municipal government and the chief of

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Please help me

Question The Orange County municipal government and the chief of police agreed on the sizc of the police force necessary for normal operations. However, they need assistance in determining the number of additional police force officers needed to cover the daily absence due to injuries, sickness, vacations, and personal leave. Records over the last three years show that the daily demand for additional police officers is normally distributed with a mean of 50 officers and a standard deviation of 10 officers. The cost of an additional police officer is based on average pay rate of $150 per day. If daily demand for additional police officers exceeds the number of additional officers available, the excess demand will be covered by overtime at the pay rate of $240 per day for each overtime officer REQUIRED If the number of additional police officers available is greater than demand, the county will have to pay for more additional police officers than needed. What is the cost of overestimating demand? (a) (S marks) (b) If the number of additional police officers available is less than demand, the county will have to use overtime to meet demand. What is the cost of underestimating demand? (5 marks) (c) What is the optimal number of additional police officers that should be included in the police force? (10 marks) (d) On a typical day, what is the probability that overtime will be necessary? (5 marks)

Explanation / Answer

Demand m mean 50 s Std Dev 10 Cu Cost of under estimating 240 Excess that needs to be paid if 1 less is asked to come Ans B Co Cost of overestimating 150 Excess that needs to be paid if 1 more is asked to come Ans A CR Critical ratio 0.615385 (Cu/(Cu+Co) So Optimal number m+Z*s 53 NORMINV(CR,m,s) Ans C Probability of sufficient number is CR 0.615385 Overtime requirement 0.384615 (1-CR) Ans D

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