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 $6.00 a box. The lettuce is sold for $18.00 a box and the dealer that sells old lettuce is willing to pay $3.60 a box. Past history says that tomorrow's demand for lettuce averages 254 boxes with a standard deviation of 37 boxes. How many boxes of lettuce should the supermarket purchase tomorrow

Answer 1

Answer:

The appropriate answer will be "289 boxes".

Explanation:

The given values are:

Cost

= $6

Sales price

= $18

Salvage price

= $3.60

Average daily demand (d)

= 254 boxes

Standard deviation ($\sigma d$)

= 37 boxes

Now,

Overage of cost will be:

⇒  $Co=Cost-Salvage \ price$

          $= 6-3.60$

          $=2.4$ ($)

Underage of cost will be:

⇒  $Cu=Price-cost$

          $=18-6$

          $=12$ ($)

⇒  Service Level = $\frac{Cu}{Cu+Co}$

On substituting the given values in the above formula, we get

                            = $\frac{12}{12+2.4}$

                            = $0.83 \ i.e.,\ 83 \ Percent$

The service level value of Z at 83% is = 0.954

⇒  Order quantity = $d+(Z\times \sigma d)$

                               = $254+(0.954\times 37)$

                               = $289.298 \ OR \ 289 \ boxes$