Skinner's Fish Market buys fresh Boston bluefish daily for $4.20 per pound and sells it for $5.70 per pound. At the end of each business day, any remaining bluefish is sold to a producer of cat food for $2.40 per pound. Daily demand can be approximated by a normal distribution with a mean of 80 pounds and a standard deviation of 10 pounds. What is the optimal stocking level?

optimal stocking level is 78.9 pound

Explanation:

Given data

buys = $4.20

sell = $5.70

sold = $2.40

mean = 80

standard deviation = 10

to find out

optimal stocking level

solution

we know here profit is = 5.70 - 4.20 = 1.50

profit = $1.50

loss = 4.20 - 2.40 = 1.80

loss = $1.80

so here

Critical Ratio = profit / (profit + loss)

Critical Ratio = 1.5 / (1.5 + 1.8)

Critical Ratio = 0.4545

so now from excel using the Norm. Inv we get Z

Z value (=NORM. INV (0.4545,80,10)

for mean 80 and SD = 10

the value of Z = - 0.11

so

optimal stocking level = mean + Z (SD)

optimal stocking level = 80 + (-0.11) (10)

optimal stocking level is 78.9 pound