4. A company manufactures tires to meet the annual demand of 125,000 production runs. One production run involves producing 100 tires. To produce the tires involves a set up cost of T. Sh 600 for general maintenance and operating time. The annual holding cost per tire is Tsh 24 if the companies manages an inventory of tires in order to stabilize production process, determine a) The number of tires that must be manufactured routinely at the least cost b) What is the minimum total inventory cost?

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

Step-by-step 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!!!

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