Assume that the total annual inventory cost for a particular item carried in inv
ID: 1131256 • Letter: A
Question
Assume that the total annual inventory cost for a particular item carried in inventory is TC(Q) = annual cost of ordering + annual cost of carrying inventory, TL/year =P* A/Q + (0.60*Q+ 150) where, P: Fixed cost of preparing a purchase order, does not depend on the quantity of the order, A: Total annual demand, Q: The number of items ordered each time a purchase order is placed. Note that A/Q gives the number of orders. a. Determine Q*, the value of Q that will minimize the total annual inventory cost. b. Total annual demand, A, is estimated to be 2,000 units and the fixed cost of P is estimated to be 15 TL per order. What is optimal TC(Q*)? c. Determine the number of orders that corresponds to Q*. d. If the fixed cost of placing a purchase order is decreased by 50%, what is the effect on Q*?Explanation / Answer
Answer for a)
We need to minimise the TC function by finding FOC
TC= P*A/Q+(0.6*Q+150)
Differentiating with respect to Q
-PA/Q^2+0.6 =0; PA/0.6 = Q^2
If we differentiate the FOC again with Q we get
PA/Q^3 that is greater than zero hence this Q will minimise TC
Q= (PA/0.6)^(0.5)
Answer for B)
Q= (PA/0.6)^(0.5)
P=15 ; A =2000
Q =(30000/0.6)^0.5= (50000)^0.5= 223.4
This is optimal Q which will minimise TC
Answer for C)
Number of order = A/Q = 2000/223.4=8.95 = 9 approx.
Answer for D)
If P=7.5
Q =(7.5*2000/0.6)^0.5=(15000/0.6)^0.5=(250000)^0.5=500