A perishable dairy product is ordered daily at a particular supermarket. The pro

Question

A perishable dairy product is ordered daily at a particular supermarket. The product, which costs $1.17 per unit, sells for $1.67 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 mu = 150 and sigma = 30. a. What is your recommended daily order quantity for the supermarket? Round your answer to the nearest whole number. b. What is the probability that the supermarket will sell all the units it orders? P(stockout) = c. In problems such as these, why would the supplier offer a rebate as high as $1? For example, why not offer a nominal rebate of, say, 254 per unit? What happens to the supermarket order quantity as the rebate is reduced? The higher rebate _____ the quantity that the supermarket should order.

Explanation / Answer

Solution:

Firsr we need to understand the meaning of rebate :

The return of part of a payment for a good. Unlike a discount, which is deducted from the price before purchase, a rebate is returned after purchase.

(a) Given that

Cost price : $1.17

Selling price : $1.67

Rebate: $1

Distribution ? = 150 ? = 30

Co = 1.17 – 1 = 0.17

Cv = 1.67 – 1.17 = 0.5

P (D ? Q*) = Cv/(Co + Cv) = 0.17/(0.17 + 0.5) = 0.17/0.67 = 0.253

For cumalative standard normal probability p = 0.253

z = 0.66

Therefore, Q* = ? + z ? = 150 + (0.253)30 = 150 + 7.59 = 157.59

(b)

P(Stockout) = 1 - P (D ? Q*) = 1 – 0.253 = 0.747

(c)

The higher rebate decrease the quantity that the supermarket should order.

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