Dear Samacheer Kalvi Students, here are the Integral Calculus II – Exercise 3.2 text book solutions in Business Maths Chapter 3 Integral Calculus II. If you have any doubts, please reach out to us in the comments section.
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Important Formulas in Integral Calculus II
Text Book Solutions for Integral Calculus I Exercise 3.1
Text Book Solutions for Integral Calculus I Exercise 3.3
Text Book Solutions for Integral Calculus I Exercise 3.4
Exercise 3.2
1. The cost of over haul 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 run for 300 hours after overhaul.
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3. The elasticity of demand with respect to price for a commodity is given by (4-x)/x where p is the price when demand is x. Find the demand function when price is 4 and the demand is 2. Also find the revenue function.
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4. 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 − 0.03×2 , the daily holding cost per scooter is ₹ 0.3. Determine the total cost for maintaining inventory for 30 days.
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5. 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. (e0.25 = 1.284) .
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6. The marginal cost function of a product is given by dC/dx = 100 −10x + 0.1x2 where x is the output. Obtain the total and the average cost function of the firm under the assumption, that its fixed cost is ₹ 500.
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7. The marginal cost function is MC = 300x2/5 and fixed cost is zero. Find out the total cost and average cost functions.
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9. Determine the cost of producing 200 air conditioners if the marginal cost (is per unit) is C’ (x) = x2 /200+4 .
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10. The marginal revenue (in thousands of Rupees) functions for a particular commodity is 5 + 3e-0.03x where x denotes the number of units sold. Determine the total revenue from the sale of 100 units. (Given e-3 = 0.05 approximately)
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11. If the marginal revenue function for a commodity is MR = 9 − 4x2 . Find the demand function.
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12. Given the marginal revenue function 4\(2x+3)2 -1 , show that the average revenue function is P = 4\(6x+9) -1.
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13. A firm’s marginal revenue function is MR =20e-x/10 (1-x\10). Find the corresponding demand function.
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14. 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.
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15. If the marginal revenue function is R'(x)= 1500 − 4x − 3x2 . Find the revenue function and average revenue function.
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16. Find the revenue function and the demand function if the marginal revenue for x units is MR= 10 + 3x − x2 .
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17. The marginal cost function of a commodity is given by MC= 14000/√7x+4 and the fixed cost is ₹18,000. Find the total cost and average cost.
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18. If the marginal cost (MC) of a production of the company is directly proportional to the number of units (x) produced, then find the total cost function, when the fixed cost is ₹ 5,000 and the cost of producing 50 units is ₹ 5,625.
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19. If MR = 20 − 5x + 3x2 , find total revenue function.
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20. If MR = 14 − 6x + 9x2 , find the demand function.
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