Applications of calculus in commerce and economics

APPLICATIONS OF DERIVATIVES IN COMMERCE
COMMERCIAL ARITHMETIC
CLASS XII MATHEMATICS

1. Applications of Calculus in Commerce and Economics Part I [email protected]

2. Total cost = Fixed Cost +Variable Cost C(x) = Cost Function R(x) = Revenue function P(x) = R(x) – C(x) At break even point, R(x) = C(x) R(x) = px where p is the price per unit x is the number of units P(x)= profit function [email protected]

3. A television manufacturer finds that the total cost of producing and marketing x television sets is Each product is sold for Rs 8400. Breakeven points are 9, 5 Determine the break even points EXAMPLE [email protected]

4. The daily cost of production C for y pens is given by i ) If each pen is sold at Rs 3, determine the minimum 2.05 y+550=3y R(y) = 3y y = 578.94 number of pens that must be produced and sold daily to ensure no loss EXAMPLE [email protected]

5. ii) If the selling price is increased by 30 paise per piece, What would be the new break even point 2.05y +550 = 3.30y 1.25 y = 550 y =440 [email protected]

6. iii) If it is known that 500 pens can be sold daily, per piece to ensure no loss Let x = the price per piece 2.05(500) +550 = 500x x = Rs 3.15 What price should the company charge [email protected]

7. Average Cost = Marginal Cost= Marginal Average Cost = [email protected]

8. The average cost for a commodity is given by where x is the output. Find i ) The total cost and marginal cost as a function of x Example [email protected]

9. Find the output for which AC increases Differentiating AC w.r.t x (x+6)(x-6)>0 -6 6 x>6 or x<-6 x>6 [email protected]

10. The demand function is where x is the number of units demanded Find the revenue function R in terms of p = p is the price per unit example [email protected]

11. Find the price and no of units demanded for which Revenue is minimum [email protected]

12. p=6 By 2 nd Derivative test, Revenue is minimum when p = 6 [email protected]

13. Substitute p = 6 x=6 Number of units = 6 [email protected]