Question

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 $8.00 a box. The lettuce is sold for $16.00 a box and the dealer that sells old lettuce is willing to pay $1.80 a box. Past history says that tomorrow's demand for lettuce averages 245 boxes with a standard deviation of 38 boxes. How many boxes of lettuce should the supermarket purchase tomorrow

Answer 1

Answer:

The supermarket should purchase 251 boxes of lettuce tomorrow.

Step-by-step explanation:

Let X = number of boxes of lettuce that the supermarket should purchase tomorrow

The information provided is:

Cost price per box = $8.00

Selling price per box = $16.00

The amount paid by the dealer for selling old lettuce per box (Salvage price) = $1.80

The mean number of boxes demanded for lettuce is, μ = 245.

The standard deviation of the number of boxes demanded for lettuce is, σ = 38.

Excess cost per box is,

$C_{E}=Cost\ price-Salvage\ price=8.00-1.80=\ 6.20$

Shortage cost per box is,

$C_{S}=Selling\ price-Cost\ price=16.00-8.00=\ 8.00$

Compute the level of service as follows:

$Level=\frac{C_{S}}{C_{S}+C_{E}}=\frac{8}{8+6.2}=0.5634$

For the service level value the z-value is,

z = 0.1596

*Use a z-table.

Compute the value of x as follows:

$z=\frac{x-\mu}{\sigma}\\0.1596=\frac{x-245}{38}\\x=245+(0.1596\times38)\\x=251.0648\\\approx251$

Thus, the supermarket should purchase 251 boxes of lettuce tomorrow.