48. Henderson Furniture sells reproductions of 18th century furniture. For a par
ID: 450341 • Letter: 4
Question
48. Henderson Furniture sells reproductions of 18th century furniture. For a particular table, the assumptions of the inventory model with backorders are valid.
D = 200 tables
per year I = 25% per year
C = $800 per table
Co = $80 per order
Cb = $50 per table per year
The store is open 250 days a year.
a. What are the values for order quantity and number of planned backorders that will minimize total cost?
b. What is the maximum inventory?
c. What is the cycle time?
d. What is total cost?
ANSWER:
a. Q* = 28.28 S* = 28.28(200/250) = 22.62 b. 28 23 = 5 tables c. Cycle time = (28/200)250 = 35 days d. TC = 89.29 + 571.43 + 473.32 = 1134.04 (using whole numbers of tables for Q and S)
* I have the answer but i need to show work
Explanation / Answer
We know that
•Optimal order quantity:
Q * = sqrt(2DCo/Ch)*sqrt{(Ch+Cb )/Cb}
Q = sqrt(2*200*80/800)*sqrt{(800 + 50)/50}
Q =6.234*4.123 =25.703 ...........Ans.
•Maximum number of backorders:
S * = Q *(Ch/(Ch+Cb)) = 25.703*(800/850) =24.19.......Ans.
Cycle time = Q/D = 25.703 / 200 =0.128 years
•Total annual cost: [(1/2)(1-D/P )Q *Ch] + [DCo/Q *] (holding + ordering)
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