Question

Can you please answer and explain this question.

Gentle Ben's Bar and Restaurant uses 6,200 quart bottles of an imported wine each year. The effervescent wine costs $8 per bottle and is served only in whole bottles because it loses its bubbles quickly. Ben figures that it costs $20 each time an order is placed, and holding costs are 25 percent of the purchase price. It takes three weeks for an order to arrive. Weekly demand is 124 bottles (closed two weeks per year) with a standard deviation of 30 bottles.

     Ben would like to use an inventory system that minimizes inventory cost and will provide a 95 percent service probability.

a. What is the economic quantity for Ben to order?

Economic order quantity=

b. At what inventory level should he place an order? (Use Excel's NORMSINV() function to find the correct critical value for the given α-level. Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to the nearest whole number.)

Hint: this is a continuous review system, similar to Alt-Cat 20.3. If you don't know how to use NORMSINV() function to find the z-value for a given % level, watch the "Hint" video by clicking the "Hint" button on the left.

Inventory Level=

Answer 1

a. Given

Unit cost =$ 8 per bottle

Ordering cost =$ 20

Holding cost =25 % of purchase price=0.25*8=$ 2

Weekly demand =124

Annual demand =weekly demand* Number of weeks in a year=124*50 (2 weeks the restaurant is closed)

Annual demand=124*50=6200

We have Economer order quantity is given by the formula,

EOQ=sqrt(2*Annual demand*cost per order/holding cost per unit per year)

=sqrt(2*6200*20/2)

=352.13

=353 (rounding off)

b.z=NORMSINV(0.95) =1.644854=1.64

We have in Normal distribution ,

z=x- /

Given =weekly demand=124

   =standard deviation=30

Solving for x,

1.64=x-124/30

we get x=173.3456 =173

Inventory level to place an order=173 bottles