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a grocer purchases coconuts for $2.85 per pound and sells them for $4.66 per pound. at the end of the sales cycle, leftover coconuts are sold for a closeout price of $1.68 per pound. the grocer purchases 10,340 pounds of coconuts. expected demand is normally distributed with a mean of 8,272 pounds and a standard deviation of 1,034.
Round your answer to two decimal places. What is the grocer's expected profit?

Respuesta :

The supermarket's anticipated profit is $1836.05

Actual order quantity.= 10340

Purchase price of coconut = $2.85

Selling price of coconut = $4.66

Calculating the cost of understocking (Cu) -

= Selling Price - Purchase Price

= 4.66 - 2.85

= 2.30

Calculating the Salvage Value-

= Purchase Price - Closeout price

= 2.85 - 1.68

= 1.10

Calculating the service level -

Cu/(Cu+Co)

= 2.30 / (2.30+1.10).

= 0.6765

As per the NORM.S.INV excel function -

NORM.S.INV(0.6765)

= 0.4579

Now,

Mean Demand = 8272 and Sd of Demand = 1034

Calculation Optimum order quantity -

Q = 8272 + 0.4579 × 1034

= 8745.46

Expected Profit -

= 8745.46 × 2.30 - (10340 - 8745.46 ) × 1.10

= 20114.55 - 1753.99

= 18360.56

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