Question

7) 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 47 pounds and a standard deviation of 16 pounds. What is the optimal stocking level? Round your answer to 2 decimal places.

Answer 1

SOLUTION:

From given data,

7) 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 47 pounds and a standard deviation of 16 pounds. What is the optimal stocking level?

* Skinner’s Fish Market buys fresh Boston bluefish daily for $4.20 per pound and sells it for $5.70 per pound.

* The remaining bluefish is sold to a producer of cat food for $2.40 per pound

* Skinner’s Fish Market's daily demand is 47 pounds with a standard deviation of 16 pounds

The shortage cost = revenue cost -purchase cost

C_s = $5.70 - $4.20 = $ 1.50

The excess cost = purchase cost - salvage cost

C_e =  $4.20 - $2.40 = $1.80

SL = C_s / (C_s +C_e) = $ 1.50 / ($ 1.50 +$1.80 ) = 0.4545

As per the table for

SL = 0.4545,z = -0.11

S_o = + z = 47 +(-0.11)(16)

= 45.24 pounds

The optimal stocking level is 45.24 pounds

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