Question

A company receives a shipment of 500 scooters every 30 days. From experience, it is known that the inventory on hand is related to the number of days x. Since the shipment, I(x) = 500 – 0.03x², the daily holding cost per scooter is ₹ 0.3. Determine the total cost for maintaining inventory for 30 days

Answer 1

Here I(x) = 500 – 0.03x²

C¹ = ₹ 0.3

T = 30

Total inventory carrying cost

= `"C"^1 int_0^"T""I"(x)  "d"x`

= `0.3 int_0^30 (500 - 0.03x^2)  "d"x`

= `0.3[500x - 0.03 (x^3/3)]_0^30`

= `0.3[500x - 0.01x^3]_0^30`

= 0.3[500(30) – 0.01 (30)³] – [0]

= 0.3[15000 – 0.01(27000)]

= 0.3[15000 – 270]

= 0.3[14730]

= ₹ 4,419