Question

A company experiences annual demand of 2,430 units for an item that it purchases. The rate of demand per day is very stable, with very little variation from day to day. The item costs $40 when purchased in quantities less than 150 and $38 for 150 or more. Ordering costs are $30 and the carrying cost is 20 percent.

a. What will be the total costs for each alternative? (Round your intermediate calculations and final answers to the nearest dollar amount.)

Total Cost

Unit cost at $40

Unit cost at $38

b. How much should the company buy each time an order is placed?

c. How much the company can save by placing the order? (Round your answer to the nearest dollar amount.)

Answer 1

Annual demand D = 2430

Ordering cost S = $30

Cost = $40 if Q<150

              = $38 if Q>=150

Carrying cost = 20%

H = 0.20*40 = $8 if Q<150

     = 0.20*38 = $7.6 if Q>=150

We calculate EOQ at each cost

Cost = 40

EOQ = 135

It is feasible as it is in the range below 150 units

Cost = 38

EOQ = 139

It is not feasible as it not in the range above 150 units

Now we calculate total cost at Q = 135 and Q =150

Total cost = Purchasing cost + Annual holding cost + annual ordering cost = CD + (Q/2)H +(D/Q)S

Q = 135

Total cost = 2430*40 + (135/2)*8 + (2430/135)*30 = 98280

Q = 150

Total cost = 2430*38 + (150/2)*7.6 + (2430/150)*30 = 93396

a) Unit cost at $50 = 98280

Unit cost at $48 = 93396

b)

The company should buy 150 units

c) Savings = 98280-93396 = 4884

Savings = 4884

The company can save 2760