Answer:
a) Economic order or production quantity = 2,500 tires.
Number of production runs in a year = 50 runs
Hence, 2,500 tires should be produced in each of the 50 runs in a year to minimize total cost.
b) Minimum total inventory cost = Tsh 30,000
Explanation:
The total cost for the tire production firm will be a sum of the total production cost and total inventory cost.
Total cost = Total Production cost + Total inventory cost
Total Production Cost = (Number of production runs in a year) × (Setup Cost of one production run)
Number of production runs in a year = (Annual demand)/(Number of units produced per production run)
Let the annual demand = D
Number of units produced per production run = Q
Setup Cost of one production run = S
Number of production runs in a year = (D/Q)
Total Production Cost = (DS/Q)
Total inventory Cost = (Average inventory level) × (Cost of holding 1 unit in inventory)
Average inventory level is usually assumed to be half of the number of units in a production run = (Q/2)
Cost of Holding a unit of product in inventory = H
Total inventory Cost = (QH/2)
Total cost = TC = (DS/Q) + (QH/2)
At minimum cost, (dTC/dQ) = 0
(dTC/dQ) = -(DS/Q²) + (H/2) = 0
(DS/Q²) = (H/2)
Q² = (2DS/H)
Hence,
Economic order/production quantity = Q = √(2DS/H)
For this question
D = Annual demand = 125,000 tires
S = Setup cost for one production run = Tsh 600
H = Holding cost for one unit in inventory = Tsh 24
Q = √(2×125000×600/24) = 2,500 units
Number of production runs in a year = (D/Q) = (125000/2500) = 50 production runs.
b) Total Inventory Cost = (QH/2)
At minimum total inventory cost, Q = 2,500
Minimum total inventory cost = (2500×24/2) = Tsh 30,000
Hope this Helps!!!