Foundation PN-3 FBMS Quiz 3

1. Given: R(x) = 3x2 + 4x + 2, MC(x) 16 = and the fixed cost is 24. Find the profit maximising value of x under perfect competition.

2. Given: R(x) = 20x² −15x −10, C(x): x²+99x+27. Find the value of x for which profit is maximum

3. Given: R(x) = 6x² −11x −35, C(x):5x² −3x +16. Find the value of x for which profit is maximum.

4. Given: R(x) = 3x² + 24x + 2, MC (x) = 42 and the fixed cost is 90. Find the value of x at equilibrium point.

5. Given: C(x) = 2x² −3x − 12, P = 33. Find the value of x at equilibrium point.

6. Given: C(x) = 900+30x+0.6x², P = 90. Find the value of x at equilibrium point.

7. A cotton mill has a fixed cost of `1540 and a marginal cost of `33. He sells a shirt at a price of `110. Find the minimum number of shirts sold so the mill incurs no loss.

8. A sugar industry has a fixed cost of `290 and a marginal cost of 50 paise. He sells sugar at the price of `15/kg. Find the quantity of sugar sold for breaking even.

9. A firm has a fixed production cost of ` 90 and a marginal variable production cost of ` 9. The price of the product is `18. Find the cost function, revenue function, and the value of Q at the Break Even point.

10. A demand function is given by: P = 1500 – 3Q and the cost function is given by: C = 12Q². Find the value of Q at the equilibrium point.

11. A revenue function is given by R= 3Q² −8Q +15 and the cost function is given by: C = 28Q. Find the value of Q for achieving highest profit.

12. The demand function is given by: P = 1400 – 25Q and the cost function is given by C = 10Q². Find the value of Q at the equilibrium point.

13. A demand function is given by: P = a – bQ and the cost function is given by C = Q². Find the value of Q for which profit will be maximum under perfect competition.

14. A tin manufacturer has a revenue function given by: R =11Q² −110Q + 70 and the cost function is given by: C = 22Q. Find the number of tins to be produced by the manufacturer.

15. A soft-drink manufacturer has a revenue function R = 7Q² −19Q +30and the cost function is given by 9Q. Find the number of cans produced by  the  firm,  under  perfect competition.

16. The result of differentiation of y = log [3x²+13x+10] is --

17. x ²/16 + y²/4 = 1      is an implicit function. The derivative of this function is :

18. y = (4x −3)³ + (5x − 2)². Calculate y1

19. Find the differential coefficient of y = e^x/e^x+1

20. When y = 4x then derivative of y is —

21. f(x)= x⁵/5 +x⁴/4+x³/2 - 7x²+18.f ' (x)=?

22. If y = xe^x then dy/dx = ?

23. limx→0{(x²- 16 )/(x - 4 )}

24. limx→0(4x² + 7x +5)

25. limx→3(x³ +1)