Question

A manager wants to minimize the total cost of the inventory. The annual demand for the wheel is 60,000 wheels, and the firm operates 240 days per year. The plant can produce of 300 wheels per day. The cost to prepare the equipment to start a production run is $150, and the annual inventory carrying cost is $3 per year. Write your answer and then Round your answer up to the nearest number for future calculation. (e.g 9.6 => 10). Please clearly write down the formulation and calculation for your answers.

Show formulas and calculations please

Questions:

2e. What is the average inventory?

2f. What is the total annual cost of producing and storing the firm’s wheels?

Answer 1

2e) Average inventory = 500 units

2f) Total annual cost = $3000

Step-by-step explanation:

2e. The average inventory is calculated using the formula;

Average inventory = Imax/2 -------------------------1

But,

Imax = Q*(1-(d/p)) --------------------------------------2

Calculating the value of Q and putting it into equation 2, we have

Q = (2DS/(H*(1-(d/p))))^(1/2)

Q = (2*60000*150/(3*(1-(250/300))))^(1/2)

Q = 6000 units

Putting the value of Q into equation 2, we have

Imax = Q*(1-(d/p))

Imax = 6000*(1-(250/300))

Imax = 1000 units

Substituting into equation 1 to calculate average inventory, we have;

Average inventory = Imax/2

= 1000/2

= 500 units

2f. Calculating the total annual cost, we have;

Annual Set up cost = n*S

= 10*150

= 1500

Annual Carrying cost = Average Inventory*H

= 500*3

= 1500

Total annual cost = 1500 + 1500

= $3000