Advertisements
Advertisements
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
Advertisements
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
APPEARS IN
RELATED QUESTIONS
Determine the cost of producing 200 air conditioners if the marginal cost (is per unit) is C'(x) = `x^2/200 + 4`
The marginal cost of production of a firm is given by C'(x) = 5 + 0.13x, the marginal revenue is given by R'(x) = 18 and the fixed cost is ₹ 120. Find the profit function
The marginal cost function of a commodity is given by MC = `14000/sqrt(7x + 4)` and the fixed cost is ₹ 18,000. Find the total cost and average cost
Calculate the producer’s surplus at x = 5 for the supply function p = 7 + x
The demand and supply functions under perfect competition are pd = 1600 – x2 and ps = 2x2 + 400 respectively. Find the producer’s surplus
Choose the correct alternative:
The demand and supply functions are given by D(x) = 16 – x2 and S(x) = 2x2 + 4 are under perfect competition, then the equilibrium price x is
Choose the correct alternative:
The marginal revenue and marginal cost functions of a company are MR = 30 – 6x and MC = – 24 + 3x where x is the product, then the profit function is
Choose the correct alternative:
The profit of a function p(x) is maximum when
Choose the correct alternative:
For a demand function p, if `int "dp"/"p" = "k" int ("d"x)/x` then k is equal to
The marginal cost of production of a firm is given by C'(x) = `20 + x/20` the marginal revenue is given by R’(x) = 30 and the fixed cost is ₹ 100. Find the profit function
