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The local supermarket buys lettuce each day to ensure really fresh produce. Each morning any lettuce that is left from the previous day is sold to a dealer that resells it to farmers who use it to feed their animals. This week the supermarket can buy fresh lettuce for $9.00 a box. The lettuce is sold for $17.00 a box and the dealer that sells old lettuce is willing to pay $5.00 a box. Past history says that tomorrow's demand for lettuce averages 258 boxes with a standard deviation of 41 boxes.

Required:
How many boxes of lettuce should the supermarket purchase tomorrow?

Respuesta :

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Answer:

276 boxes

Explanation:

Given the following :

Cost price of lettuce = $9

Selling price of lettuce = $17

Selling price of old lettuce (Salvage value) =$5

Mean demand (m) = 258

Standard deviation(σ) = 41

The marginal profit = selling price - cost price

Marginal profit = $(17 - 9) = $8

Marginal loss ; old lettuce : cost price - salvage value $(9 - 5) = $4

Probability (p) = marginal profit /(marginal profit + marginal loss)

P = 8 / (8 + 4) ; 8 / 12 = 0.667

Using the InvNorm function of the T84 calculator :

InvNorm(prob, mean, standard deviation)

InvNorm(0.667, 258, 41) = 275.697 = 276 boxes

Number of lettuce boxes supermarket should purchase tomorrow = 276 boxes

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