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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?

Respuesta :

Answer:

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

Tundexi

The optimal stocking level is 78.9 pounds.

The Optimal stocking level pertains to the point where the total excess cost and total shortage cost curves intersect each other because the total cost is lowest at that point and leads to profit maximization.

Given data

Buys = $4.20

Sell = $5.70

Sold = $2.40

Mean = 80

Standard deviation = 10

Shortage /Underage cost (Cu) = $5.7 - $4.2

Shortage /Underage cost (Cu) = $1.5

Excess of Overage cost (Co) = $4.2 - $2.4

Excess of Overage cost (Co) = $1.8

Critical Ratio (CR) = Cu / (Cu + Co)

Critical Ratio (CR) = $1.5 / ($1.5 + $1.8)

Critical Ratio (CR) = 0.4545

Corresponding z value = NORMSINV(0.4545)

Corresponding z value = -0.11

Optimal stocking level = µ + zσ

Optimal stocking level = £80 + (-0.11)*£10

Optimal stocking level = £80 + (-£1.1)

Optimal stocking level = 78.9 pounds

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