Ray’s Satellite Emporium wishes to determine the best order size for its best-se
ID: 325155 • Letter: R
Question
Ray’s Satellite Emporium wishes to determine the best order size for its best-selling satellite dish (Model TS111). Ray has estimated the annual demand for this model at 1,000 units. His cost to carry one unit is $10 per year per unit, and he has estimated that each order costs $25 to place. The purchase cost is $500 per unit.
For the order quantities Q = {25, 50, 75, 100, 125, 150}, find the annual setup ordering cost (S*D/Q), holding cost (H*Q/2), purchasing cost (C*D), and the total annual cost (including the purchase cost) Report the results for order quantity 25 in Answersheet (3 points).
Report the Q value with the minimum total cost (select from the list in cell B12) and the corresponding total cost in Answersheet (2 points).
Explanation / Answer
To be calculated:
For each given order quantities, Q = {25, 50, 75, 100, 125, 150}
Annual Setup cost
Holding cost
Purchasing cost
Total annual cost
Given values:
Annual demand = 1,000 units
Holding cost = $10 per year per unit
Setup or Ordering cost, S = $25
Purchase cost, C = $500 per unit
Solution:
(a) Order quantity, Q = 25
Annual Setup cost (S*D/Q) = 25 x (1000 / 25) = $1000
Holding cost (H*Q/2) = (10 x 25) / 2 = $125
Purchasing cost (C*D) = 500 x 1000 = $500,000
Total annual cost = Annual Setup cost + Holding cost + Purchasing cost
Total annual cost = $1000 + $125 + $500,000
Total annual cost = $501,125
(b) Order quantity, Q = 50
Annual Setup cost (S*D/Q) = 25 x (1000 / 50) = $500
Holding cost (H*Q/2) = (10 x 50) / 2 = $250
Purchasing cost (C*D) = 500 x 1000 = $500,000
Total annual cost = Annual Setup cost + Holding cost + Purchasing cost
Total annual cost = $500 + $250 + $500,000
Total annual cost = $500,750
(c) Order quantity, Q = 75
Annual Setup cost (S*D/Q) = 25 x (1000 / 75) = $333.33
Holding cost (H*Q/2) = (10 x 75) / 2 = $375
Purchasing cost (C*D) = 500 x 1000 = $500,000
Total annual cost = Annual Setup cost + Holding cost + Purchasing cost
Total annual cost = $333.33 + $375 + $500,000
Total annual cost = $500,708.33
(d) Order quantity, Q = 100
Annual Setup cost (S*D/Q) = 25 x (1000 / 100) = $250
Holding cost (H*Q/2) = (10 x 100) / 2 = $500
Purchasing cost (C*D) = 500 x 1000 = $500,000
Total annual cost = Annual Setup cost + Holding cost + Purchasing cost
Total annual cost = $250 + $500 + $500,000
Total annual cost = $500,750
(e) Order quantity, Q = 125
Annual Setup cost (S*D/Q) = 25 x (1000 / 125) = $200
Holding cost (H*Q/2) = (10 x 125) / 2 = $625
Purchasing cost (C*D) = 500 x 1000 = $500,000
Total annual cost = Annual Setup cost + Holding cost + Purchasing cost
Total annual cost = $200 + $625 + $500,000
Total annual cost = $500,825
(f) Order quantity, Q = 150
Annual Setup cost (S*D/Q) = 25 x (1000 / 150) = $166.67
Holding cost (H*Q/2) = (10 x 150) / 2 = $750
Purchasing cost (C*D) = 500 x 1000 = $500,000
Total annual cost = Annual Setup cost + Holding cost + Purchasing cost
Total annual cost = $166.67 + $750 + $500,000
Total annual cost = $500,916.67
Answer:
Order quantity with minimum total cost, Q = 75
Minimum total cost = $500,708.33
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