A supplier of MacoriX Inc., offers the following discounts according to the amou

Question

A supplier of MacoriX Inc., offers the following discounts according to the amount of the ordered,

OPTION          AMOUNT          DISCOUNT %           UNITARY COST

1                      0-999                0%                              $5.00

2                     1000-2649         4%                              $4.70

3                     >= 2650            6%                              $4.25                

MacoriX provides the following information: Annual Demand=5000 units, Unit Cost=$49, and Holding Cost=20%/unit/year.

a. What is the amount of products that should be ordered and the total annual cost?

b. If you need 10,000 units, how many order per year should be done to reduce the total cost of acquiring the units?

c. If the company can only hold an average of 4,750 units, would your conclusions change?

Explanation / Answer

Annual Demand(D)=5000 Ordering Cost(O)=49 Holding Cost(H)=20% *5=1/unit/yr a)EOQ=Sqrt(2*D*O/H)=sqrt(2*5000*49/1) Q= 700 TC=D*O/Q+H*Q/2+P*D Order size Total Cost 700 TC=5000*49/700+1*700/2+5*5000 25700 1000 TC=5000*49/1000+1*1000/2+4.7*5000 24245 2650 TC=5000*49/2650+1*2650/2+4.25*5000 22667.45 Hence based on the discount offered order size should be 2650 at a total cost of 22667.45 b) for 10000 units orders=10000/2650= 3.773585 ie. 4 orders c) since the average inventory at the order size of 2650 is 2650/2=1325 ie. Lesser than 4750 hence the conclusions shall not change

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