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 – 0.0

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

Sum

Solution

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

shaalaa.com

Application of Integration in Economics and Commerce

Is there an error in this question or solution?

Q 4 Q 3 Q 5

Chapter 3: Integral Calculus – 2 - Exercise 3.2 [Page 72]

APPEARS IN

Samacheer Kalvi Business Mathematics and Statistics [English] Class 12 TN Board

Chapter 3 Integral Calculus – 2
Exercise 3.2 | Q 4 | Page 72

RELATED QUESTIONS

The cost of an overhaul of an engine is ₹ 10,000 The operating cost per hour is at the rate of 2x – 240 where the engine has run x km. Find out the total cost if the engine runs for 300 hours after overhaul

An account fetches interest at the rate of 5% per annum compounded continuously. An individual deposits ₹ 1,000 each year in his account. How much will be in the account after 5 years. (e^0.25 = 1.284)

The marginal cost function is MC = `300 x^(2/5)` and fixed cost is zero. Find out the total cost and average cost functions

Find the revenue function and the demand function if the marginal revenue for x units is MR = 10 + 3x – x²