Question

HW Score: 63.08%, 41 of 65 pts Score: 0 of 8 pts 16 of 20 (12 complete) Question Help Problem 12.53 University of Florida football programs are printed 1 week prior to each home game. Attendance averages 75,000 screaming and loyal Gators fans, of whom two-thirds usually buy the program, following a normal distribution, for $4 each. Unsold programs are sent to a recycling center that pays only 20 cents per program. The standard deviation is 10,000 programs, and the cost to print each program is $1. Refer to the standard normal table for z-values. a) What is the cost of underestimating demand for each program? Cs (round your response to two decimal places). b) What is the overage cost per program? Co .8round your response to two decimal places) c) How many programs should be ordered per game? programs should be ordered per game (round your response to the nearest whole number)

please solve c

Answer 1

The selling price of the program = $4

The cost to print each program = $1

The salvage value of each program = $0.20

The cost of overestimating demand or overage (C_o) = Cost price per program - Salvage price per program

= 1 - 0.2

= $0.8

The cost of underestimating demand or underage (C_u) = Selling price per program - Cost price per program

= 4 - 1

= $3

We will now calculate the critical ratio and will use the value to find the Z statistic value from a normal distribution table.

Critical ratio = C_u / (C_u + C_o)

= 3 / (3 + 0.8)

= 0.7894

The Z statistic for a critical ratio value of 0.7894 is 0.80 which we will use to calculate the number of programs that should be ordered so as to maximize expected profit

The mean of demand = Two-thirds of 75000

= 50000

The standard deviation of demand = 10000

The number of programs that should be ordered per game so as to maximize expected profit = Mean + Z * Standard deviation

= 50000 + 0.80 * 10000

= 58000 programs