Question

A supermarket buys lettuce each day from its supplier. Each morning any lettuce that is left from the previous day is sold to a dealer. The supermarket can buy lettuce for $4.00 a box. The lettuce is sold for $10.00 a box and the dealer pays old lettuce $2 a box. Demand for lettuce follows a normal distribution with a mean of 250 boxes and a standard deviation of 34 boxes. How many boxes of lettuce should the supermarket purchase each day?

Answer 1

The number of boxes of lettuce the supermarket should purchase = 273 boxes

Explanation:

This is a case of understocking and overstocking.

We are given;

Cost price = $4 per box

Selling price = $10 per box

Salvage value = $2

The formula for cost of understocking is;

C_u = S.P - C.P

Where;

C_u is cost of understocking

S.P is selling price

C.P is cost price

Thus;

C_u = $10 - $4

C_u = $6

Cost of overstocking is given by;

C_o = Cost Price - Salvage value

C_o = $4 - $2

C_o = $2

Now,

P(D ≤ Q) = C_u/(C_u + C_o)

P(D ≤ Q) = 6/(6 + 2) = 6/8 = 0.75

From the z-table i attached, the z value of 0.75 is approximately 0.67

Thus;

The number of boxes of lettuce the supermarket should purchase =

D + (z-value x standard deviation)

We are given;

D = 250

Standard deviation = 34

Thus;

The number of boxes of lettuce the supermarket should purchase = 250 + (0.67 * 34) = 272.78 ≈ 273 boxes