Question

A perishable dairy product is ordered daily at a particular supermarket. The product costs $1.16 per unit and sells for $1.75 per unit. If units are unsold at the end of the day, the supplier takes them back at a rebate of $1 per unit. Assume that daily demand is approximately normally distributed with μ= 155 and σ =35.

Required:
a. What is your recommended daily order quantity for the supermarket?
b. What is the probability that the supermarket will sell all the units it orders?
c. In problems such as these, why would the supplier offer a rebate as high as $1?

Answer 1

a) 174

b) 21.33%

c) The supplier will offer a rebate as high as $1 because the supermarket orders higher quantity of goods and also in order to encourage the purchase of goods by the supermarket.

Explanation:

product cost = $1.16 per unit

sell price = $1.75

Rebate = $1

Daily demand : μ = 155 , б = 35

a) Determine the recommended daily order quantity

shortage = sell price - cost = 1.75 - 1.16 = $0.59

Excess ( overage ) = cost - rebate = 1.16 - 1 = $0.16

service level = shortage / ( shortage + excess ) = 0.59 / ( 0.59 + 0.16 ) = 0.7867

therefore the Z-value = 0.8 also Mean value = 150 , std = 30

note : values gotten from Appendix table

∴ Recommended daily order quantity = Mean + ( z * std )

= 150 ( 0.8 * 30 ) = 174

b) Determine the probability that the supermarket will sell all units ordered

= 1 - service level

= 1 - 0.7867 = 0.2133 = 21.33%

c) The supplier will offer a rebate as high as $1 when the supermarket orders higher quantity of goods