What is the Economic Order Quantity (EOQ) for this product? How much could the firm save annually in total holding and ordering costs by ordering at the EOQ level?

BUSADM 370 Introduction to Supply Chain Management:

Homework 3 (50 points):

For all the problems, you must show your complete and accurate work to receive full scores. If you only provide the final answers without showing your computations, even your answer is correct, you will not be assigned a full score (or if your answer is wrong, you will miss the opportunity of receiving any partial credit).

Problem 1) (12 points)
A produce distributor uses 3,200 packing crates a month, and each crate is purchased at a cost of $12. The manager has assigned an annual carrying cost of 30 percent of the purchase price per crate. Ordering cost is $270. Currently the manager orders once a month.
a) What is the Economic Order Quantity (EOQ) for this product? (4 pts)
b) How much could the firm save annually in total holding and ordering costs by ordering at the EOQ level? (8 pts) (Show the computations for the total holding and ordering costs in detail)

Problem 2) (14 points)
A manager has just received a revised price schedule for its main product from a vendor as seen in the table below. What order quantity should the manager use to minimize total costs? Annual demand is 45,000 units, ordering cost is $100, and annual carrying cost is $4 per unit (regardless of the price per unit).

     Quantity                       Unit Price
       1 to 999                               $12.75
       1,000 to 1,999                   $12.50
      2,000 to 2,999                  $12.35
      3000 or more                    $12.25

Problem 3) (12 points)
a) Compute the multifactor productivity measure (output in sales dollars) for each week using the data provided below to produce chocolate bars. Assume 40–hour weeks and an hourly wage of $18. Overhead is 1.25 times the total weekly labor cost. Material cost is $48 per pound. Standard price to sell is $150 per unit. (10 points)
    Week         Output (units)            Workers           Material (lbs)
       1                   3,500                              6                      1,200
       2                  3,750                              7                      1,275
       3                  3,875                              7                      1,350
       4                  4,000                             8                     1,425
b) What do the productivity figures suggest? (What is the trend?) (2 point)

Problem 4) (12 points)
Organic milk is stocked at a grocery store each week. At the end of each week, unsold organic milk price is reduced by 25% and the store can sell the unsold organic milk fully at this lower price. If weekly demand for organic milk is normally distributed with a mean of 200 gallons and standard deviation of 20 gallons, find the price for which a fresh gallon of organic milk sells. Assume that the store has a service level of 95% and purchases organic milk for $6.1 per gallon.

Bonus Problem: (6 points) (Bonus points will be added to your homework score).
A fish distributor is trying to perfect his business to maximize the money he saves. Daily fish sales are normally distributed with a mean of 350 pounds and standard deviation of 60 pounds. The distributor sells each pound of fish for $6.00 and pays $2.50 per pound to buy fish. The distributor must get rid of unsold fish by paying a waste removal facility fee of $0.25 per pound of fish. How many pounds of fish should the distributor order each day and what % of the time will he experience a stock–out? Are there any drawbacks to the order size proposed and how could the fisherman address such issues?