Answer:
The supermarket should purchase 251 boxes of lettuce tomorrow.
Step-by-step explanation:
Let <em>X</em> = 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, <em>μ</em> = 245.
The standard deviation of the number of boxes demanded for lettuce is, <em>σ</em> = 38.
Excess cost per box is,
![C_{E}=Cost\ price-Salvage\ price=8.00-1.80=\$6.20](https://tex.z-dn.net/?f=C_%7BE%7D%3DCost%5C%20price-Salvage%5C%20price%3D8.00-1.80%3D%5C%246.20)
Shortage cost per box is,
![C_{S}=Selling\ price-Cost\ price=16.00-8.00=\$8.00](https://tex.z-dn.net/?f=C_%7BS%7D%3DSelling%5C%20price-Cost%5C%20price%3D16.00-8.00%3D%5C%248.00)
Compute the level of service as follows:
![Level=\frac{C_{S}}{C_{S}+C_{E}}=\frac{8}{8+6.2}=0.5634](https://tex.z-dn.net/?f=Level%3D%5Cfrac%7BC_%7BS%7D%7D%7BC_%7BS%7D%2BC_%7BE%7D%7D%3D%5Cfrac%7B8%7D%7B8%2B6.2%7D%3D0.5634)
For the service level value the <em>z</em>-value is,
<em>z</em> = 0.1596
*Use a <em>z</em>-table.
Compute the value of <em>x</em> as follows:
![z=\frac{x-\mu}{\sigma}\\0.1596=\frac{x-245}{38}\\x=245+(0.1596\times38)\\x=251.0648\\\approx251](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%5C%5C0.1596%3D%5Cfrac%7Bx-245%7D%7B38%7D%5C%5Cx%3D245%2B%280.1596%5Ctimes38%29%5C%5Cx%3D251.0648%5C%5C%5Capprox251)
Thus, the supermarket should purchase 251 boxes of lettuce tomorrow.