Univ of Florida football programs are printed 1 week prior t

Univ. of Florida football programs are printed 1 week prior to each home game. Attendance averages 90,000 screaming and loyal Gator fans, of whom 2/3 usually buy the program, following a normal distribution, for $4 each. Unsold programs are sent to a recycling center that pays only 10 cents per program. The standard deviation is 5,000 programs, and the cost to print each program is $1.

If needed or possible, please round to the nearest ten thousandth.

(1) Find Cu. (2) Find Co. (3) Compute the optimal service level. (4) Find the z-score that corresponds to the optimal service level. (5) Compute optimal order quantity. (6) Suppose the university wishes to ensure a 95% service level. Find the new z-score and compute the new optimal order quantity.

Solution

The cost of overage = cost of low sale =$ 1 = C_o

Cost of underage = cost of lost sale = Price - cost of overage = C_u

= 4 - 1 + 0.10 = $ 3.10

Now, point estimate of sales = 2/3 * 90,000 = 60,000

Optimal service level = Point Estimate X (1 – ((cost of overage – cost of underage) / price))

= 60000 ( 1 - (1.0-3.10)/4 )

= 60,000 ( 1 + 0.525)

= 91,500

Z-score = (91,500 - 90,000) / 5000

= 0.3

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